Excothermic . . . ?

" The microbial action in decomposition is exothermic, which means that heat is a by-product of the chemical process of breaking down the material. "

Winter composting has some different considerations than warm weather composting.
Remember that it is a tender, living, ecosystem, in constant transition.
We still want things to continue cooking, but ambient temperatures significantly slow the process down.  ( Think of food in your frig . . .  )
Air flow is always an important factor, but during the winter, we will not be turning the compost pile.  Let it stand and insulate itself, with the ' brown matter ' you've added  (Fall's leaves . . .  ).
Resist the temptation to cover the pile with a tarp, or anything that is non-porous.
To insulate the compost pile, use bales of wheat straw to surround the pile, during particularly cold periods.  ( Here at our Garden at Kashi Atlanta, the compost pile is wrapped in landscape fabric, which may be enough during our usually mild winters.)
When adding fresh ' green ' matter to the pile, make sure that the particles are small, for easier breakdown.
Winter winds can rapidly dry out a compost pile, so some watering of it may be necessary. 
Observing the activity going on in the compost pile is very valuable !  

When there is steam, there is compost cooking.