if you look at https://www.nps.gov/yell/planyourvisit/parkroads.htm it says all the roads that close (there is one that stays open year round) are scheduled to close on oct 31.

I don't think one storm will put down enough snow that they have to close the roads, I think it will be based on schedule. They have the plows and equipment necessary to handle one storm as I'm sure they've had plenty of big storms in their open season before. So I think you are good until oct 31

there was a recent thread that recomended https://guidealong.com/tour/yellowstone-national-park/

just got back from there last night. Was fantastic. No crowds. Crazy warm (although it won't be this weekend).

If you have a getoutpass, and you're going the west yellowstone way, hit up bear world on your way up.