FFF,
Carb ice occurs because of two effects.
One is the latent heat of evaporation of the fuel reducing the temperature of the (water vapour bearing) inlet air.
The second is where the airflow drawn through a venturi by manifold depression causes an increase in the velocity of the air past the throttle plate and hence a reduction in inlet air pressure and hence its temperature (Bernoulli's Law) in that immediate vicinity.
If the air reaches its icing point, the obvious will occur. Note that summer air (thunder storm weather) holds more water by weight than drier winter air, so icing in aircraft may be more acute on summer days .
The two effects combined have the potential to cause icing around the throttle venturi. Aircraft are prone to it because they have a forward facing intake duct and operate in air that is conducive to ice formation; namely cool but humid air.
A smaller throttle setting gives a more intense pressure drop than a wider one so yes, lower power makes carb ice more likely. Also, a lower throttle setting makes the consequences more serious because the actual throttle aperture is smaller and is likely to become blocked rapidly. High speed (generally, at least on a fixed pitch prop) = more prop RPM so lower MAP.
The answer is to use carb heat on a regular basis, iaw the Flight Manual.
