DM said:
My point didn't address cold temperatures.
I don't want to belabor this, but I do want the information in here to be correct. You said:
Water will not evaporate in cold temperatures...
...which certainly is "address"ing cold temperatures, and just plain isn't true. And it seems like you still believe it to be true, because:
How do air molecules provide heat energy to the water molecules in cold temperatures? They do not have enough kinetic energy.
...that's the same as saying "water will not evaporate in cold temperatures" (now talking about the mechanism) and it still isn't true.
This is getting more into chemistry, but I'm pretty sure the mechanism of evaporation (or sublimation, which Dave brought up) is that air molecules with high kinetic energy (which there are, even in a cold environment because the atmosphere is one big billiards table, with a bell curve of kinetic energies for individual particles) will "knock off" molecules from the surface of the water/ice. At the same time, some water molecules with a low kinetic energy will be deposited on the surface of the ice. Depending on temperatures and relative humidity, there may be either a net inflow (precipitation) or outflow (evaporation, sublimation) of water molecules.
So even if you have water just above freezing or ice somewhat below it, at the same temperature of the air above it, the air above it
will (depending on humidity) provide the heat necessary to cause sublimation or evaporation.
Don't assume the water molecules (or even ice molecules) are colder than the surrounding air, this could lead a small percentage of kinetic energy from the air molecules to contribute to vaporisation.
In fact, because of evaporation/sublimation, the temperature of water or ice in equilibrium will always be slightly lower than the temperature of the air (very slightly, but still...). The molecules that get "knocked off" first are the ones with the highest kinetic energy, lowering the average kinetic energy of the water/ice.