Disclaimer: I am a super newb here.

I and two of my daughters are planning some hiking around Wyoming next Summer. I would like to include some back country backpacking into the route. Some of this terrain will include crossing mountain passes above 10,000 feet, specifically Antoinette Peak and Cache Peak in the Gros Ventre range in late June . I would like to also consider Sugarloaf and Elk Mountain in Medicine Bow Forest in Early June. I have looked at the historical snow depth for these mountains and others that we may cross and there is a good chance of there being snow still at the peaks.

Most of the time, we will be hiking along at about 6,000 feet in warmer weather. How would you recommend packing for this variation? I am trying to pack as light as possible. But I don't want to get into a situation where we are in a pickle because we didn't bring the right gear. I was thinking ice axe, one 90M rope and carabiners and switching from trailrunning shoes to hardier boots. Your thoughts please?

Have any of you summitted any of these peaks in June? What gear did you use?