Cold air is more dense so you have to move a greater mass of air out of the way. At anything above 12 mph drag is the main issue on a bike. It varies with the square of speed. Twice as fast, four times the drag.
Air density is important enough to have the world hour record set in Mexico City (alt 2300 m).
You also breath in a greater mass of air but that makes little difference if you don't have the capacity to supply it to your muscles. This is the principal behind an intercooler in a car. It's like a second radiator but only has air in it. Cold air is more dense so the greater mass can support more combustion. There may be other thermodynamic benefits to do with how heat engines work but I'm not sure how important that is. My turbos have intercoolers. It's important for them because the turbo compresses the air and raises the temperature so the intercooler brings it back down.
Anywho, you don't have much chance to make use of the denser air because there are other limiting factors so more drag becomes an issue.
Generating heat on a bike is not likely to be a problem in cold weather unless you move very slowly. Shedding heat is a more common issue.
As well as skeletal muscles you generate heat from brown fat, liver any other muscular contraction and... the brain.