To climb in altitude is to progress toward fall or winter. It may be July at 3,000 feet, but climb beyond 9,000 feet, and it's more like September or later. Travel high enough, and snow can fall on any day of the year.
Watch weather forecasts, and be aware that rain below is likely to be snow above.
High altitude promotes rapidity of change. During summer, be prepared for all increments of weather, from hot to cold, dry to wet, sleet, wind, and snow.
Rain gear must be accessible at a moment's notice, and that nice warm vest you brought along has no value if it's buried so deeply in a pack that you can't access it without major delay.
Rainy weather points toward wool and synthetic fleece, materials that retain insulating properties even when wet. Cotton and down are worthless when soaked.
Prepare in other ways, as well. Does your horse allow you to don a rain slicker while mounted? Is it safe to do so, even with the wind whipping the garment around? Take the time to train him at home, not when you're in a tight spot.
Lightning is a major worry at high elevations. Again, watch the weather forecasts. If you get caught up high during a thunderstorm, try to get down to lower elevation as quickly as possible. Avoid shelter under an isolated tree. Also, you're probably safer off your horse than on him, since your profile is lower.
(For more on how to cope with extreme summer weather on the trail, see The Trail Rider, July/August '12.)