Rabbits, birds, squirrels, raccoons, moles and deer do not hibernate during the winter. Instead of hibernating, these animals do other things that help them adapt to the cold weather such as migration.
The most common alternative to hibernation during the winter is migration. Animals such as elk and birds migrate when the weather gets too cold. These animals can travel thousands of miles to get away from the cold and will often return to the same spot they were in when spring comes. Their migration spots are generally the same every winter.
Animals who do not hibernate during the winter have other methods of survival like growing extra fur to help them deal with the cold temperatures. This fur is able to help insulate them from the outside, but many animals also take on extra fat during the winter to help insulate them from the inside. This insulation allows them to go about normal activities during the winter months and allows them to be protected from extremely cold temperatures.
While not all animals hibernate, there are many that will take short naps and spend more time in their homes than others, such as moles and squirrels. They will stay in their trees or in the ground where it is warmer during the winter. They will only come out from their areas when they need food or for extreme circumstances.