As someone in Europe, the last two posts were more or less correct.
I've done SLC on a budget. And arguably, if the OP is looking for powder powder powder til you puke, that's probably the best place in the U.S. to do it.
The deals are there, and means are there. What I do:
1. Take the bus from the airport downtown.
2. Stay downtown, you can get reasonable, but basic digs at places like Super 8.
3. It's a block or two walk to the public transit to the Cottonwood Canyons.
4. The ski rental shops have discounted tickets.
5. Don't bother with the Snowbird tram, IMHO not worth it. Peruvian takes you nearly there.
So, you don't need a rental car (that's what, 200-300 per week).
The ski bus is easy to use, if you don't mind adhering to a schedule, and getting up a bit early to catch it.
There you go.