Are you talking about snow camping/hiking, or just backpacking in rainy Washington in the winter?
The Paradise area at Mt. Rainier is a great and safe place to learn and practice snow camping, assuming the road stays open this year. There are several areas within easy walking distance that people camp in. Snow caving or tent camping are interesting and enjoyable. You need a 4 season tent, and a warm sleeping bag and insulating pad. A shovel is also a necessity, even if you're tent camping. You also need a way to travel on snow, such as skis or snowshoes.
There are good chapters on snow camping in Mountaineering, 7th edition, for more info. Good luck.