We went on the first northbound cruise of the season offered by the cruise line we chose. Tom's right, the scenery was spectacular, which it always is, but probably made more so by the snow on the mountains. The weather we had was cold, as we expected - probably 50s during the day on cloudy days, 60s on sunny days. Standing on the bow of our (small) ship most of the day, we had to wear many layers, including winter-weight clothes and windbreakers, but of course had to peel about half of them off when we went inside!
If the sun was out (about half the time on ours), and we were out of the wind, we were comfortable in sweatshirts, maybe with a fleece vest worn over that. We had rain in Ketchikan (again, definitely expected) and on a few other days for part of the time. We were told later that this was one of the colder Mays they had had in southeast Alaska!
We had no issues with going that early in the season. We saved money, as prices are of course higher from June through August, and saw everything we wanted to see except orcas - I believe they normally get to Alaska just a bit later in the season. Plenty of humpback whales, though, and we saw sea otters, puffins, bears, etc.
Another advantage of the earlier cruises is that you may have fewer cruise ships in any given port - which means only 2500-4000 tourists walking around, instead of upwards of 6000!