I went to June Lake in mid-October for 10 consecutive years. We had snow 3 times...about a 1' each time.
One year there was a lot of wind with it but we had no problem getting to June Lake or up in to Tuolumne and out to Lower Cathedral Lake.
Altitude resistance is another story entirely...I can do anything local without chemical but...overnight is another story. I take Diamox, if my overnight location is 8,360' or above.