Jesus... I feel like I can deal with extreme cold better than most but it's just fucking stupid cold right now. You'd be able to unload your gear at the gate but I'm not sure about parking there. What you might have going for you is it's so cold nobody wants to deal with driving up there and ticketing/towing you. Parking at Brighton could work but would still be a bit of a bitch walking back up/down. It's a pass so the wind can really rip up there but you should be able to find some thick pines to shelter yourself a bit. After this last storm you might even be able to build some sort of snow shelter.
I dunno... I love the sense of adventure and would normally be on the same page, but this is one of those weeks a shitty hotel in Midvale/Sandy just seems necessary. Would allow you to actually enjoy the skiing without being sleep deprived and drained the entire day because your body used all of its energy trying to keep you circulating/alive at night.