Dave,Carburetor ice can form under most conditions, weather or not visible moisture is present, and weather or not the temperature is near freezing. Carb ice is very common in humid conditions at temperatures approaching one hundred degrees Farenheight.
Yes, fuel injected engines ice, though obviously not at the carburetor...they don't have one. Induction ice is not uncommon in the winter, when flying in freezing rain, or in conditions conducive to surface icing. These aircraft don't have carb heat, but will have an alternate air source which may be manually or automatically activated. (Automatic alternate air is normally "sucked" open by low manifold pressure, and is usually termed a "suck door.").
Without a carb air temperature gage, carb heat must be applied full-on any time carb ice is suspected, or it is suspected that carb ice may form. There are times when the application of carb heat may cause carb ice to form, or assist in the formation. Additionally, as you identified, airflow is not filtered entering the engine during operations with carb heat engaged. All carb heat is, in most applications, is an alternate door that blocks airflow from the filter, and opens directly into the engine compartment.
The operating engine temperature determines how warm the air is that can enter the carburetor with carb heat on. After an extended descent at idle, for example, little heat is available from the engine; certainly far less than might be available when operating at a higher power setting and slower airspeed.
Carb heat is anti-ice protection, not de-ice protection. It's not there to remove ice (though it can), but to prevent it. Carb heat can remove small amounts of ice. However, a big limitation of carb heat is that once ice forms such that the engine is choked or stopped, there's little one can do to remove the ice until it melts on it's own. I've seen many frustrated pilots who executed forced or precautionary landings with partial or complete power failures, who were embarrassed because they couldn't duplicate the cause of the failure. They were unable to restore power until after their landing...and then the engine ran just fine. Why? The ice had melted.
Carb ice forms as a result of a pressure and temperature drop occuring across the carb venturi. This drop is necessary and the main principle on which the carburetor operates. In the center of the carburetor is a narrow construction which causes the airflow to increase in velocity (up to or more than 300 mph at this single point, at full throttle), and causes the pressure to drop (bernoulli's principle).
When the pressure drops, fuel is drawn out of the float chamber in the carburetor, into the airstream. There it's vaporized and mixed with the air, and then it flows into the intake manifold and the combustion chambers in each cylinder. As the pressure drops, so does the temperature. Ambient air temperatures in the high 90's can quickly drop below freezing. As the fuel vaporizes, moisture is introduced. Moisture is also introduced from the ambient atmosphere. The warmer the atmosphere, the more water vapor it can hold.
The best time for carb ice to form is at lower power settings on the ground when little heat is available, the throttle plate is closed, and only a little ice is necessary to cause airflow disruption through the carb. The second best time for it to form is during the initial power application following a prolonged power off descent. I've seen pilots make forced landings following a go-around; the engine quit as power was applied, or shortly thereafter, and the aircraft was forced to land.
The reason for this is ice had formed during the descent. This ice formed the base for a more rapid formation, on a larger scale, as the throttle was opened to go around. This could have been prevented in part by making a power on approach, by exercising the throttle on approach, by using carburetor heat on approach, and by delaying shutting off carb heat until go-around power had been applied.
Part of the preflight runup checklist requirments for all carburetor equipped piston engine airplanes, is a carb heat check. Most pilots simply apply carb heat for a couple of seconds to see that they can note a RPM drop. This is a mistake. Carb heat should be applied for 10-15 seconds at a minimum. The check isnt' just to check that warm air is reaching the engine, but to determine that no ice had formed, and any ice that has formed, is melted.
I prefer to do the carb heat checks on the runway just prior to releasing brakes, so that the very minimum of time for ice to buildup elapses before going to full power. If you do your carb heat checks in the runup area and then have several minutes before takeoff, seriously consider doing another check just prior to, or on the runway. Ice could have formed in the meantime, and that can be costly.
Water can remain in a liquid state to temperatures as low as -40 deg (c/f). Water vapor may be readily available at even low temperatures, though a common wives tale persists that cold air is too dry to form ice. Not true. In fact, use of carb heat at low temperatures in some cases can induce icing. The conditions under which this occurs are rare; it doesn't happen often, but it can happen. The safest rule of thumb for aircraft not equipped with carb air temperature gages is to use carb heat regularly and whenever necessary.
For aircraft equipped with carb air temperature gages, carb heat may end up being used throughout the year at partial settings as required, to maintain the carb air temperature at the proper setting.
I've experienced carb ice in most phases of flight, from takeoff to landing, to cruise, to ground operations while taxiing. I made a forced landing during a descent out of instrument conditions in a Cessna 182 years ago, due to carb ice. (When I applied the carb heat, the control came away in my hand, having failed. I exited the cloud base with enough altitude to set up a landing on a small gravel strip, and walked away). Also on a number of occasions, I've experienced iced spark plugs; this typically is only a problem during starting.
Go with the manufacturers recommendations. I absence of specific direction, I prefer to apply carb heat in the pattern about midfield, and leave it on for tent to fifteen seconds. I'll make the initial power reduction abeam the numbers, and then shut off carb heat. If I have any inclination that carb ice may be required, I will leave it on throughout the approach. In such circumstances, during a touch and go landing, or a go-around, I prefer to leave carb heat on until initial power application has been made. If operating at more than 75% power in a normally aspirated engine, carb heat should be shut off before reaching 75% power. If operating above 3,000' or higher on a standard day, the engine can't make 75% power even at full throttle, so this isn't an issue. If you fly near sea level, use your best judgement.
Use of carb heat at high power settings on higher compression engines can cause engine damage and detonation by overheating the intake air. If using carb heat at higher power settings, the mixture should be enrichened. The mixture is automatically enrichened during carb heat application, because the heated air is less dense, resulting is a richer mixture). If high power settings exist, manual enrichment is necessary to protect the engine, cool the mixture in the cylinder during combustion, and to reduce the liklihood of detonation.
During normal prolonged use of carb heat at less than high power settings, and any time operating at less than 75% power, a good rule of thumb is to lean the engine while carb heat is applied. If you're only applying carb heat for a few moments, leave the mixture alone. However, if you're going to make a cross country flight with carb heat engaged, lean for it; same for a prolonged descent.
An example of this may be a reduced power descent through clouds or visible moisture in a carbureted engine. Manifold pressures and/or RPM as appropriate, should be closely monitored. I always strongly recommend against power off descents (except for certain training emergency simulation scenarios); this is one good reason why one should avoid them.
If you don't have them, you should get hold of the manufacturers recommendations on engine operation for the aircraft you fly. You can get the general information fromthe aircraft flight manual/pilot operating handbook, but this information is watered down and dummed down, and isn't written by the engine manufacturer. You can contact Continental and Lycoming directly for their recommendations, supplied in a booklet form. You should also refer to the maintenance manuals for information on your aircraft systems, propeller, engine, etc. Much of the good information you'll find there, won't be found in the traditionally used pilot sources.
Good luck!!