And I've done it second half of June on multiple visits to Utah. But even then you do have to play a little hopscotch with snow patches and slip through one long snow field. Goats seem very active in June, which is fun. If you can hold off to the 15th or so, you'll be plenty fine just borrowing some slip-on crampons, assuming it's a fairly normal year. Then you won't have to play the slippy slidey game like me.