Well you can go crazy with paper snowflakes for starters! Hang them on strings from the ceiling, but make sure they're not banging into your face all the time.
How about really cheap wrapping paper? Could be effective to cover a wall in a sparkly silvery colour?
Cotton wool balls on thread also looks like snow.
Buy cheap netting fabric (maybe the charity shop has some) (is it tulle I mean?) and cut it into long jaggedy icicle shapes - they can hang down over the windows and doors.
Fairy lights, obviously. You could use your own and just take them home over Christmas (depends how committed you are to the decorating I suppose!)
White sheets on the ground to look like snow? (Don't know if that would be a safety issue though - suppose you could tape them down?)
Could you do something with the lighting... you can get a pack of 30 odd LED tea lights, which are really safe, that you could dot around the room? You can even get ones that flicker, you could put them in lanterns? (if you happen to already have lanterns, or you can make paper lanterns pretty easily).
Large boxes wrapped up as presents? Or would the children get excited and think they were actual presents?
Paper chains made out of old magazines= free and pretty easy to make.
If you're feeling fancy you could get a snowflake cutter and make salt-dough snowflakes and then cover them with glitter glue and hang them up... or different shapes... gingerbread men?
Pine cones are free! Plus holly, although you'd have to de-berry it to make it safe for little ones...
All the 'polar-themed' teddies you can find? Penguins, white teddies, etc?