I know it varies but Rule of thumb, what time of year do these parks start getting snow? I mean Enough to impact travel and close roads and portions of the parks?
It really depends, we got snow in Glacier in August (not much) but the Howe Ridge fire impacted travel more than anything this year. Pretty much kept the west side of going to the road closed the majority of the season. They usually don't get the going to the sun road plowed and opened until around mid June.
Well studded tires are legal in Montana Oct. 1- May 31, unrestricted in Wyoming if that tells you anything... .I've seen enough snow in Yellowstone in early October to impact driving conditions for sure.