I've ridden in the Colorado Rockies a few times. Mid June, late June, early July, and early September. All 1 to 2 week rides. The June rides all had good weather. The numerous passes had good weather. Nothing extreme for rain or snow or cold. Pleasant riding. The July ride had some unpleasant weather. Going from Idaho Springs to Dillon over Loveland Pass. It snowed a couple miles from the top and a couple miles down the other side. Hard snow and windy. And cold. But pleasant weather in Idaho Springs and Dillon, the valleys. The September ride had rain and cold on Red Mountain pass and in Silverton. But pleasant weather going from Silverton to Durango after a day of rest holed up in Silverton.
The weather in mid to late June in the Rockies can vary from sunny, warm and wonderful to cold, rainy, snowy and miserable. But even if the weather is awful at the passes, it does not last long. Half hour or so before the top and then 10 minutes of descent. And the 30 minutes or so of climbing isn't bad because you are generating plenty of body heat. I went over Loveland Pass in the snow and cold with just shorts, short sleeve jersey and a garbage bag wind vest put on at the top. Wasn't ideal, but I made it. No gloves, no balaclava, no tights, no jacket, no booties. I would advise carrying a wind/water proof jacket though.