ah, the Salt Lake City Shuffle, and all in one day!
On arrival it would be a good idea to go to the rental car desk first, then grab your luggage, then haul your luggage to your car in garage. If there are two of you one of you would go to rental desk while others grab luggage and wait on the Arrival island. The driver would have to exit the airport and loop around and pick-up at Arrival island.
Snowbird is the closest resort to airport, although Alta is only a few minutes further. Once you get out of airport, there are plenty of exits with shopping centers where you can park with some room, unpack, organize and dress for skiing.
When driving back to the airport, drop your luggage off with the bell cap at the Departure island, before you drop your car off, (you'll have to loop around airport to get back into rental garage) although there may be a fee if you don't have the proper credit card program.
If you are at Snowbird and flight is at 5pm, you could easily ski to 2pm, giving yourself 15 minutes to stop at parking lot in SLC and change, then 45 minutes to drive to airport for 3pm. But if it's snowing you should give yourself 30 minutes extra to get down the canyon. (or even an hour if its' a heavy snowfall)