Why don't trees freeze solid in the winter time

Or do they? Seems to me that ice crystals would pierce the cell walls of the tree, thus killing it. So if they don't freeze, what keeps them from freezing?

You're right; if trees get too cold in winter, they will suffer damage and might die. Trees cope with low temperatures through a variety of mechanisms, like leaf drop, water loss management, and (what you're really asking about) acclimation.
Acclimation causes the desaturation of fats within the cell (think of the difference between unsaturated olive oil and saturated butter, and how they act under low temperature), and the accumulation of solute molecules inside the cell (which, if you know your chemistry, means that the freezing point of the cell will be lowered). Trees also use some of the properties of water to stay alive; liquid water can absorb a lot of heat energy, and it even releases heat as it freezes (called the "enthalpy of fusion"). By managing where water freezes within it, the tree can both control how much damage is done by freezing water, and also take advantage of the small amount of heat released by the freezing water. However, this only works so well; all trees can be killed by temperatures that get low enough.

They store and produce heat via photosynthesis

Mythbusters did this myth.

It turns out that trees sap contains a type of Anti freeze.