Looks like a decent road trip. Bryce, Zion and the GC are something else when snow covered. The color contrasts highlight how amazing those areas really are. Shoot even the Tetons right now on a clear day are just plain badass. There's not much in Twin Falls but the gorge, so hopefully you're visiting someone there, or you might be disappointed.
The parts I marked in red are areas that would be slow going if a storm were pushing through. Getting off I-80 in Evanston WY headed north will get a serious pounding by weather and winds. The area around Bryce can get pretty snow covered, and with it being a rural area can take longer to get plowed. That's based off my experience living and recreating near both areas. Out by Victor, Driggs, up through Island Park and West Yellowstone they hit those roads hard with snow removal as it's a main thoroughfare through that area. Mostly 2 lane highways with passing lanes. Any of those places would be alright in my opinion a day or two after any major storm.
How soon are you making this trip? I say take either or really. My daughter rallies here FWD car with snow tires and has never had an issue yet. The Subaru with AWD sounds better, but without good tires that AWD isn't really that big of a deal over the fwd. Just my 2 cents.
Give yourself extra time through those red areas, make sure you top off on fuel, and have some extra snacks, water and blankets in case you need to hunker down for the night un-expected. It's not Antarctica, but it can get treacherous for a day or two until things get cleared up. Each of those states have real good 511 highway apps, I'd download them and keep checking on updates as you go.
I'm in Idaho Falls, and have a place available in Island Park. If you want, I can send you my number in case you get in a bind through that area, you can hit me up.
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