The distance of your trip, coupled with the fact that you have to either cross the Rockies *and* the Sierras (or go around them) mean that you have no time for unplanned diversions or delays. IMO, you have a pretty tight schedule there.
That said:
You can run into snow anywhere from the Plains westward. You can run into snow on I-40 through ABQ and Flagstaff, you could take US-50 and have clear sailing, you could take I-80 and flip a coin. It is very difficult to tell these things as far out as five or six days. Storm predictions along the Rockies are hard to nail down even only three days out.
The best advice I can give you is avoid going across the Divide on I-80 through Wyoming. It is deservedly notorious for foul weather in winter... having driven it many times (sometimes with a loaded trailer behind me), it can be more “entertaining” than one might like about eight months out of the year.
The WX along US-50 is usually pretty dry. That’s why that area (from the CA/NV border east to Pueblo, CO) is high desert. They simply don’t get much precip along that area of the country. But there are huge stretches where there is no help for 10’s to 100+ miles if you break down on US-50. And there are many areas along US-50 with no cell coverage as well.
I’ve moved my trip further south, and I’ve truncated the itinerary at Phoenix. See map at post 33.