In many areas of the US, including much of the Southeast, Southwest and Pacific coast, winter camping is not a drastic departure from camping at any other time of the year. But, in the high country and mountains where snow is bountiful there are a few things you can do to make sure you are comfortable and safe while traveling over and camping on snow.
When going into the field in snowy conditions you must first consider how you are going to travel. If it's early spring and the snowpack is shallow or hardpacked you might consider just hiking in your sturdy leather boots. If the snow is less consolidated you should use snowshoes or crosscountry skis to travel. You can usually expect to do about two mph on snowshoes and about four mph on skis over level terrain. Also, consider that your route will be significantly less obvious than simply following a packed or blazed trail during the summer months. Be sure that you have a good map and even better compass. Take turns breaking. Keep a steady pace that prevents you from sweating too much then getting chilled when you stop to rest. And, if you are in avalanche country, make sure you know enough about snow dynamics to keep yourself safe.
Respect the fact that mountain weather can change quickly and it can be severe. Make sure you pack enough clothes and gear to stay warm and comfortable, and enough food to last an extra day or two in case you are pinned down by a storm.