Mount Hood in Oregon has summer skiing. They do snowbaord and ski camps all summer long. It's basically a glacier that has snow year round. You'd probably end up wearing a long sleeve shirt or maybe a hoodie.
I was going to suggest Mt. Hood too. I haven't been yet but they do have camps during the summer. I had a friend visit in high school and he came back with an awful (he thought it was cool) google tan so be sure to wear sunscreen!
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