Most PCTers hit the JMT in the third week of June. The classic start date is June 15th from Kennedy Meadows.
When I did the PCT in 2006, I also went in that window. But it was considered a very heavy snow year and "unpassable". So, I'd equate it to late may/early june in an average year. Someone calculated that on the JMT section, we hiked about 70 snow miles.
It was outstanding fun to walk on all that snow!! PCTers were the only ones out there for the southern two thirds. Often, we'd practically jog along the snow because it was easier to keep up momentum. The sun cups weren't all that bad. The creeks were all doable, but very very dangerous.
I was one of the few that carried an ice axe and crampons (made by ULA). Many carried ice axe only. I wouldn't go without one, but I'd strongly consider BD's whippet. I self arrested and saved myself serious injury once. And I put the crampons on twice but didn't really need them. Definitely hike in shoes that do well when wet, as my feet were soaked for the entire time.
If you want to read more about what it might be like, go to trailjournals.com and read journals from 2005 and 2006 PCTers.
Of course, disclaimers apply. Don't do it if you're a newb.