You don't have to have real special stuff. Layers is the key. My family makes a snow ski trip once a year (going this weekend actually!). I got my daughter some "bibs" and a Lands End coat from a consignment sale. When she outgrows it I'll resell it at the same sale.
We also got some tights for my daughter to wear. So, she will have tights, jeans, t-shirt or other thermal undershirt, a sweater, and her coat. Along with gloves & mittens, and a hat.
You might be able to find stuff on sale. There are several stores that select things on sale. Not sure if you have time to order something online, but you can check dealnews.com for sales & deals. Otherwise, check your local Dicks Sporting Goods, Sports Authority, etc for sales!
(I'm in Alabama, so I don't know what you have near you!)