DON'T try to burn a fire in an open windy area, or directly on the snow. These are two recipes for disaster. If you must build fire in the open, build wind blocks. If building a fire over snow, cut some green wood to build a fire platform.
DO check your hands, feet, face, and ears often for frostbite. Carry a staff or walking stick to check the depth of the snow. Build snow shoes to travel more efficiently, especially in deep snow.