No way dude! June is one of the best months for Tuolumne! The valley is just starting to get real hot at that time, while temps can be awsome up higher. Sure there might be some snow, but so what!? Just bring good shoes and maybe a light weight alumi axe.
Plus the snow pack this year is extremely weak. There will be mimal coverage by June, mostly just under the North Faces.
Also, June is a great time to hit the fun Snow Couloirs for some alpine flavor. The Dana Couloir is a fun jaunt. As well as the coiloirs on North Peak in the Coness area. Climb granite until your arms and skin are trashed then go run up some fun bueatiful peaks via the nice corn snow.
September/October in the high Sierras is cold and dry. Spring time is the best if you ask me, except for the bugs. The mosquitoes can be vicious in June depending on the year.
Go for it Distel, I will be there from mid-june through mid-july and am looking for partners to hook up with. Have fun!
Whatever... I guess it is a matter of opinion... The road is normaly closed till June right??