All trees go dormant whether they lose their leaves or not. Typically, trees start to go into dormancy around November and come out of dormancy around April. Of course it can vary slightly from year to year. 

This is the time you want to trim your trees. The trees have reabsorbed the nutrients from their leaves and therefore trimming their branches won't be as much of a shock to their system. Also, with the weaker sun, your trees will be less likely to get sun scalding if trimmed in the winter. Sun scalding is like a sun burn resulting in the bark peeling and causing scarring. Sometimes the tree will try to protect itself by pushing out a bunch of sprouts to shield itself from the sun.