Snow coverage in the Sierra is far below normal this year, so by the end of June, you will have no trouble heading up to Matterhorn.
Man... that brings back memories. I did a x-country hike starting at Twin Lakes, past Matterhorn (climbed the summit on day 2), then through the northern reaches of Yosemite, coming out via Mattie Lake and Glen Aulin to Tuolumne Meadows. That was all back in 1972!