I’ve backpacked almost all the trails in the San Jacintos over the years visiting relatives in Idyllwild. Snowcover depends, of course, largely on the amount of snowfall that winter and how high you intend to hike. You will be able to get reasonably good information from the San Jacinto National Forest Ranger Station, or the San Jacinto State Forest Ranger Station located in town. I can Remember being in ankle deep snow in March on the trail up to Taquiez Peak. In terms of temps, it can get down to freezing at night but the days can be quite pleasent and dry. But it is high country and you should have the gear for cold, wind and wet. Unless you are an experienced high country hiker, a trip all the way to the peak of Mt. San Jacinto itself could be rather risky from a wind and variable weather point of view.
Talk with the rangers, they will give you the low down. By the way, The ranger station that is located directly across from the Mexican restaurant (sorry, can’t remember weather it is the state or national) in my experience tends to be much more helpful than the other one.
If you have the time, a really nice trip is to start at Hwy 74 (thats the road from town down to Palm Springs)on the PCT and hike up to the Saddle Junction and back down Devils Slide trail into town. That, as I remember, is about 38 miles including side trails to water. That for me was two and a half pretty tough days, but you start down in desert like terrain and work your way up into and through an alpine paridise. The trail along the side of Murray Canyon is beyond discription! Quite a varied trip. If you have the experience highly recommended! But it has the potential to be quite cold and windy.
Razor