I'm not even asking about the Cottonwoods roads bc I've heard they are treacherous. I'm hoping to avoid taking UTA, but is that a likely necessity if we get a foot or so of powder on any given day?"
Trying to figure out how you made those two sentences back to back? Sounds like you answered your own question.
Also why are you staying in Salt Lake if you're planning on skiing everywhere but and worried about driving? It seems like you'd be much better off staying in Park City or Ogden area, if the CCs are last on your list.
The route to Park City is not really flat. Wide yes (interstate highway), but it does climb over a mountain pass and can get pretty hairy in the snow.
Snowbasin is a wide county road that usually gets cleared quickly. On Sundays and holidays, though, they don't seem to get it cleared very effectively. It's not super steep, but it's steeper than anything you'll find in a lot of states. I believe it's a 7 or 8 percent grade on the Huntsville side, not sure about the other side, but it's also hilly.
Another option would be to drive to Eden through Ogden and take the shuttle to Powder. That would be your flattest option, mostly interstate highway. The shuttle is like $3 and takes you up the nasty stuff.
Outside of that, it really depends on your comfort level. If you're not used to driving around on steep, hilly terrain in the snow, get chains or get a 4WD and rest a little easier. Personally, I'd say if you have to ask, you'd be better off in a 4WD. I've seen people get stuck in their small 2WD on the little hill right outside of Snowbasin. Driving 2WD in the snow seems like an unnecessary adventure, particularly if you have a group (i.e. split the cost of an upgrade).
The likelihood that it will be bad is pretty low. If it snows overnight, they tend to get things cleared pretty quickly. If it's bad or you're worried it will be, hop on the UTA up the CCs and avoid driving. Then drive up to Snowbasin or Powder the day after - they should still have plenty of snow.
Also don't get too excited for that storm - forecasted storms have been disappearing into thin air all winter. Way too early to rely on that one.