Yes.. they do run better and make more HP... this is the time of the year when dirtbike riders come back from a ride and say.... "man.. my bike was just running SOOO crisp in this cool air!"
Cooler air is more dense... so it is like you have a 60cc engine... because there are more air molecules in a given volume at lower temps.
But another reason.. is that the carburetor sends fuel to go with the air... but now that there is more air... it is now leaner... so it is now running the way it always would if you jetted it correctly for the weather all the time... (in other words they are really a little too rich for max HP in hot weather).
Modern fuel injected vehicles with little computer sensors and controllers all over the place don't do this so much... because the computer takes into account the air temp (and other things) all year long... and is adjusting the air/fuel all the time.