A tale of 2 pistons

gripper said:

I thought engines performed better in cold weather (and damp) because the air is more dense and so dense air carries more fuel with it. (some gas turbine engines use water methanol to do this)

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Cold, (thus denser) air has more oxygen molecules per volume, and carburetors mix air/fuel by volume, so the cold air makes it leaner. The "run better" legend is (usually) true because jetting generally has a safety margin built in (richer than optimum) to allow for variations in altitude, temp., usage, thus forfeiting a small degree of power for engine safety. The "runs better" is real & noticeable because, when cold, dense air is at hand, you are now closer to optimum.

The major benefit from using methanol fuel comes from the way it freezes the inlet tract. The incoming air evaporates the fuel and the high latent heat of vaporisation of the fuel causes the air to chill and become more dense, so more fuel is needed to make the mixture right and the process repeats until a balance is reached.