Snow Fort or Igloo
Get your whole family involved and build a snow fort or igloo. An igloo requires a certain kind of hardpacked snow capable of making strong blocks so a snow fort might be a bit easier. You can pile snow up with shovels and then dig out the fort or build up walls. Get your kids involved and let them help to "engineer" the fort. Use a spray bottle to help mold the snow. Be sure the kids are involved in building the fort as well as playing in it afterward as building it is the best (and most tiring) part.
You may not have snowshoes, but that doesn't mean you can't build them. This is another great project that will get your children's minds working as they have fun in the snow. All you need is a sapling for each foot and some string and sticks. Spend some time crafting the snowshoes with your children and then go outside and test them out.
A nature walk around the yard, woods or neighborhood can be done with or without the aforementioned snowshoes. Take your kids on a walk in the snow to look for animal footprints. If you have a footprint guide, bring it along to help identify any tracks that you find. If not, it's a great opportunity for your kids to use their imagination--even a cat or dog footprint could appear to be made by an exotic animal!
Snow Ice Cream
As fun as snow is to play in, it can be even better to eat. Making snow ice cream is best done by leaving a bowl outside to collect the falling snow, since snow on the ground may be dirty and you don't want to encourage your children to pick snow up and eat it (they probably do this enough on their own). Once you've collected ample snow, simply mix it with simple flavoring like syrup or vanilla and a little milk and you have a frozen treat. Alternately, make a snow cone by just adding flavored syrup. Encourage your children to try out different flavors and make it a fun experiment in cooking.
Setting Up Camp
Pretend that your children are actually deep in the great outdoors and need to gather supplies to set up camp. Have them search for things like sticks to build a fire, food and water. These items could be gathered from natural sources around the yard or planted by you in a snow day scavenger hunt. Building a snow fort for shelter could also be part of the activity. Let your children use their imaginations to decide what they'll need and how they'll set up camp.
Snow is an excellent medium for art. It can be used to sculpt great creations or used as a canvas to draw and paint. You don't have to limit your kids to snowmen and snow angels, let their imaginations take over and they can craft all kinds of things. Different types of animals can be easily crafted from snow. Use spray bottles to pack the snow and add a little food coloring to allow the children to "paint". Children can even draw in the snow with a simple stick.