Toddlers have all in Ones like snow suits but you can get waterproof ones. They are fleece lined. Bushbaby, or search for baby ski wear. I have a muddy puddles suit totally waterproof ! Def get snowboots. Mothercare did cheap ones last year or Clarks do them. Get an eBay habit! If only to sell them next year (just after christmas when everyone wants snow gear!!)
Bush Baby stuff is fab! We had a 10 days or so of -12 last winter (W Yorks), luckily I had just got DS some snowboots from another MNer. Worth every penny at twice the price. Their shop is near us, but the Little Trekkers website is very good too.