I've climbed Shasta in every month of the year, but weather has kicked my butt more times than I care to admit. I've been blown off in May and I've had beautiful weather in February. Study the weather and snow conditions carefully just before you go.
I’ve climbed the north side of Shasta a couple weeks ago and it was a wonderful trip. The glaciers were kind of icy but still OK to descent safely. I’m planning to go there again over the next two weeks.