How much snow you encounter depends on the year and when you start your hike. Most hikers begin hiking the PCT at the end of April, with the intention of reaching the Sierras in mid-June. This usually works so that there is snow only at the passes - a few miles each side - which you can ease by planning your days so you reach the passes mid to late morning, when the snow has softened enough that it is easy to dig your boots and ice axe into it, but not so soft that you are postholing with every step. Usually one pass a day works well, through the Sierras, though you may find yourself doing two on a few days. In a normal year, snow is only an issue for a couple of hundred miles - Forester Pass to Sonora Pass. And for most hikers who reach the Sierras in mid/late June it isn’t an issue for very long.
Just be aware, in some years, especially El Nino years - you may run into a lot of snow on the trail, almost continually for a couple of months, instead of the normal two weeks or so that most hikers see. 1993, 1995, and 1997 were high snow years. We had friends who carried their ice axes the entire way from Campo to Manning. If you are really uncomfortable with snow travel, and won’t be able to get some experience in the meantime, then pay attention to snow levels to decide whether you really want to do the PCT in 2006 or not.
That said, I had no experience at snow travel when I did the CDT, and we ran into snow regularly for the first two months. We had axes and used them, both to prevent falls and for attempted self-arrest. When we did the PCT I was comfortable with snow travel and had a harder time with snow melt than icy snow. But we were early reaching the Sierras (June 2) and so our experience was quite different from that of people a week or two behind.
On the issue of crampons - they allow you to hike over icy passes earlier in the day - but have their own dangers. Cindy Ross blames crampons for Todd’s broken leg. YMMV
Spirit Walker