SIM cards are strangely resilient. I had mine submerged in the ocean for 25 minutes (left phone in my pocket), and it worked fine forever.
I wouldn't turn it on in a few days though, unless you live in a really dry climate in addition to having the phone in rice. Water or moisture can take a long time to dry up, and it's really the only thing that shorts the motherboards in electronics. If you don't wait long enough, starting it up again if there is moisture inside could ruin it.
But since you found it in snow and were able to turn it off in the first place, you'll most likely be ok. Wish I had the same story for my MBP. ;'[