Mr Hawk,
Remember the ole formula:
Lift=CL 1/2 Rho Vsquared S ??
Well on a colder day, the air is more dense. Therefore the Density part of the formula (Rho) is greater.
Whilst this does achieve more engine thrust, even if this is flat rated, you do get more air flowing over them wings.
Therefore the climb performance does increase markedly, unless the cold weather means that the pilots drank more through the winter to pass away those cold lonely nights, and put on a few extra pounds, which negated all the above..
Hot weather will decrease the climb performance (almost to Nil climb angle) when you are out in the desert on a very hot day.
Strangely enough, the desert heat didn't stop me drinking the nights away either...