The good thing about camping in the snow is that you won't impact the environment as much -- since it's coated in a cold, white cushion. The bad thing is that that cold, white cushion is hard on your body. With a few simple tips, though, you can set up a campsite that will keep you safe and warm even during the darkest depths of winter.
Many of the same factors that influence summer campsite selection will affect the decision in the winter. You can camp on the snow or on any bare ground showing through the snow, but not if it's supporting significant plant life. As with summer camping, you should choose a relatively flat spot so you and your sleeping bag won't slide downhill in the middle of the night. Consider camping in the sun for warmth and avoid depressions where cold air may settle. Wind can be a real problem for winter campers as well. If you see hard, sculpted snow with a frosty, brittle texture, that means this an area where wind is frequent and conditions are harsh. Loose, powdery snow is a bad sign, too -- it means that the wind has deposited snow here and your tent would be covered quickly. Avoid both of these types of areas.
Snow hazards should definitely be considered. Foremost among these is avalanches. Before you go camping, check with your state's avalanche prediction center and consider staying at home if the threat is high or extreme. When you're on the trail, look around for trees that have been mowed down by an avalanche and for piles of avalanche debris pushed into the canyon below you. These are signs you should move on before pitching your tent. Other hazards include crevasses, or deep cracks that form in glaciers, and cornices, or overhanging masses of hardened snow that form at the top of steep mountain ridges.
As long as you avoid these hazards, your snowy campsite should be a comfy winter wonderland -- if perhaps a chilly one. And you can settle in for few days of skiing or snowshoeing, and a couple nights of starry skies.