In a lot of years, the first big winter-type storms will start in late September. These can be multi-day storms with a lot of precipitation.
This year, the first storm hit on September 18th and brought snow down to 5,000' and a lot of cold rain below that. We were lucky to finish our CDT hike that day. Other folks a couple of days behind us ended up having to road walk through the park.
If you're ahead of the storms, the great. If not, it would make for an unpleasant trip.