White fleece fabric? As in a cheap throw blanket. (I've used green and brown for no snow versions of the ground.)
Suzukovich uses white throw carpets if you look back a few years. I like that better as the snow is deep and more ’solid' looking than the "misty" look of typical display snow. (Some misty stuff here and there on the rugs looks better yet though)
Cleaning those should be easier than cleaning fluff fabric too. Vacuum and/or toss in the washing machine. (use a hose vacuum with a nylon over the wand, leave about 5 inches of toe hanging, hold tight. Any little items accumulate in the wand caught in the nylon, and 99% of actual dust passes thru.... some hairs etc picked out quick as you recover those things you didn't really want to suck up. ...and they are clean of dust now too 
)
Stars... I'm a huge fan of glow-in-the-dark things and even painted some mow-critter headlights/tailights with it. Stars would work with it too if they get enough light each day. .
There is another way, using light. First option is holes in the sky for tiny Christmas bubs to stick out.
Some of the controllers for blinking ones have a "random" setting today too.
Or, still using Christmas bulbs or one or two other types, attach to the main backdrop to light it. (it is now a support). You need to create a top lip, or "curtain rod" support to create a gap between what is drapped off the rod or lip, and the bulbs/support.
Use heavy, dark blue or black satin opaque cloth for a light blocking curtain and hide everything.
Now put tiny (tiny) holes in the cloth (near but not over some, Left, right, above, below, etc. and/or right over others with sm. bulbs, creates variety of bright and dim stars.
Curtain sides, top, bottom can be attached to the support to block escaping beams of light. Don't use real hot bulbs without adding some venting to the support (Two 3 sided rectangle boxes over a hole, open side down if you're using kinda hot lamps, i.e., don't make an easybake oven out of it
(this is loosy how the night sky background on some stages at Showbiz/Chuck E. Cheese was done. I always liked the effect they got. We also made similar concept drops for theaters when I was a stage and light grip. Some solid, some curtain based. Usually the drama dept wouldn't get good enough cloth without a big push for it early on before the budget was drained by uneeded fancy paints, or pizza, etc.etc.)
