Take Them Skiing or Snowboarding.If you are fortunate to live close to a ski resort, skiing is a fun family sport that can really build memories. Skiing for locals is often available at a reduced rate as well.
Consider Showshoeing. A less expensive sport for people in snowy areas, showshoeing offers some fun opportunities. The nice part about snowshoeing is that almost anyone who can walk can showshoe. And showshoes are comparatively inexpensive to rent or buy. There are many places around that lend themselves to beginning showshoeing. At the GORP site, one of the best outdoor sports sites on the Net, you can find information about snowshoeing and about good locations for the sport.
How About Ice Skating? Not everyone will be a Tara Lipinski on skates, but many families enjoy ice skating together during the winter season especially. Skating takes a little practice and steady ankles are pretty important, but it is a sport that is adapted well to the beginner. Ice rinks are found in many localities in the winter, and there are also many indoor skating facilities.
Tubing or Sledding Can Be Fun. One winter activity our family has really enjoyed is tubing and sledding. In areas with snowy climates, there are often good tubing hills around which are safe but exciting. More and more municipalities are building storm detention ponds in and around parks, and these are very good sledding locations. Purchasing an inexpensive plastic toboggan, a sliding disk or even the famous "Flexible Flyer" is the place to start. Then dress them warmly and head to your favorite hill.
Snow Painting: A Great Idea. Some of our friends have taken up snow painting as a fun family activity. All you need is a few water bottles with a squirt top, some water and food coloring and some snow. Fill each bottle with water and some food coloring and then head outside. A little imagination and some creativity will result in some great works of art.
Igloos and Snow Caves. If you have lots of snow, it can be fun to build a snow shelter like an igloo or snow cave. We have often used aluminum bread pans as a brick mold for an igloo. For ideas and techniques about igloos, check out About Landscaping Guide Dave Beaulieu's guide to igloos. And the High Adventure Girl Scout's site offers a pictorial step by step process for making a useful snow cave.