I was there last January when they had, and were getting, way more snow than they're getting now. I went ahead and paid extra to rent a Toyota Tundra 4x4, which handled very well in the snow (I didn't even have to weigh down the bed).
I also chose to go ahead and buy chains at Les Schwab in Portland. If you don't wind up needing them, you can just return them afterwards.
I would not chance it without 4wd or chains. It gets pretty hairy up there, and I saw a lot of people that weren't going anywhere without chains.
Edit: I should also add, those without chains or 4wd were SERIOUSLY pissing the rest of us off by causing huge traffic jams. Whenever we saw a cop roll up to ticket them, everyone rolled down their windows from the traffic jamb we were in and clapped. Don't be that person.