There are a couple of ways to get the ingredient necessary to make fake polymer snow. You can purchase the fake snow or you can harvest sodium polyacrylate from common household sources. It is non-toxic but do not let the kids purposely eat it.
You can find sodium polyacrylate inside disposable diapers or as crystals in a garden center, used to help keep soil moist.
All you need to do to make this type of fake snow is add water to the sodium polyacrylate. Add some water, mix the gel. Add more water until you have the desired amount of wetness. The gel will not dissolve. It's just a matter of how 'slushy' you want your snow.
You can put it in the refrigerator or freezer to make it more like snow.
If you want to change it's color just add food coloring.