mev

I remember ~2 inches of snow on a backpacking trip in Colorado in August. At high elevations you can get this even in summer. However, by September you start to get into shoulder season. Storms can come through or it can be nice, somewhat unpredictable.

While crossing the Americas in 2016/2017, I left Banff on August 18th and came across Yellowstone September 7th and then back across Fremont Pass in CO on September 24th. I delayed my trip across Fremont Pass for a day to let an early snow storm pass. Photo below shows it was still cold, but fortunately clear again.

Overall by September, you'll have more probability of storms you likely want to avoid, perhaps with a delay. October will make it more likely.

If it were me, I'd probably start in the west first to get across the Cascades and Rockies earlier...