My husband and I cruised Princess to Alaska with his family in mid-May a couple years ago. It rained every single day including the day we were on the bus from Seattle to Vancouver. Still friends of ours from Colorado cruised early May and noted weather was very nice...light jacket and sweater kind of weather.
Not sure this can help you at all since it is pretty conflicting but at least it is input. Happy cruisin!
We have been to Alaska 5 times. Our 1st cruise was the end on June and it was to warm, not what we expecting of Alaska. Since then we have cruised the middle of September. Chilly, but not unbearable..what you expect Alaska to be, we enjoy it everytime we go - great shopping - end of the season and the merchants want to get rid of their inventory. Great prices!!
We sailed the Island Princess northbound cruisetour starting September 4th, 2004 and had a great time. It was cool and sunny in every port (Ketchikan, Juneau, Skagway) until we got to cold Fairbanks on the land portion--about 18 degrees in the morning for the gold mine tour. Still, all we needed most of the time for comfort was a light windbreaker. Also, it snowed in Denali and at the Denali Princess Lodge. The lodge workers said it was the first snowfall of the season.
I have some photos if you would like to view them. There's a few shots of the Denali snow.
We cruised to Alaska on the Star Princess in July, 2003. I brought all sorts of clothes with me and I'm glad I did. We sailed out of Seattle, and much to our surprise, it was gorgeous in Seattle: Sunny and warm. That was it though. I think we saw sun in Victoria Canada towards the end of our cruise, but all the ports in Alaska were cloudy or misty. I'd say the temps were about 50-60 degrees. It wasn't cold, but with the rain, etc. it felt raw. As long as you dress layered, you can always take things off if you get warm. It's beautiful in Alaska however so you don't even realize that the sun rarely shines. However, I have heard where some folks have had luck with the sun. It's breathtakingly beautiful and you will NEVER forget this cruise. Have a wonderful trip!!