don't build it on a throne for one.

what are utah winters like where you live? certainly park city winter is very different than slc winter.

if you deal with a fair amount of snow as I would assume, here's my list of advice:

the absolute best type of bike you could do this with is a single speed 29er, but ss 26" or 27.5" mtbs, or ss cyclocross bikes will do fine too. preferably a frame with lots of tire clearance, relaxed geometry, and disc brakes. despite the rust factor, I'd still recommend steel, the compliance makes riding over bumby ice sheets and unplowed roads a lot more comfortable. the larger the wheel diameter the better, even just six inches of fresh wet snow will make a 26" wheel stop dead. 29ers have a much better chance of rolling through it, and even that couldn't get through the worst of it here.

build it on a bike with clearance for at least 35mm tires, and get the burliest, knobbiest tires you can fit into your frame.

mountain bike riser bars, a nice upright position and wide cut bars (at least 600mm) will make for better stability and leverage on snow, ice, and slush.

fenders, self explanatory

water-resistant lower layers, your wheels will be kicking up a lot of wet gritty slush on the warmer days, even with fenders, your feet and legs will get wet, dress for it.

ride slow, ride ahead of yourself, and be prepared to go down occasionally - ice ruts will get you.