Cruises to Alaska aren't much different during the season.
Early cruises sometimes are better because the locals haven't gotten tired of all the tourists. Some area might be open for the ships to cruise to .Late May or early June the weather can be warm or cold or anywhere in between.
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IMHO, late May is one of the best times to cruise to Alaska. The last few cruises is September tend to have the most chance for rain and cooler temperatures. The bid plus, is that there a lot of good sales available at the end of the cruising season.
I still much prefer cruising to Alaska in mid to late May.
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I cruised the last weekend in May and I loved it we saw lots of whales. However, we didn't see any bears, I was lead to believe this was because the salmon were not running. I didn't mind missing the bears, I wanted to see the whales and it was a good time of year for that. I hope that helps.
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The fringe season, early to Mid May and after the first week of Sept, can often have significant weather drop offs, with the worse potential weather of the Alaska season, so it does make a difference in my opinion. I no longer sail these timeframes since they don't discount them like they used to .
From mid August on, you are running into more rain. Overall you need to be well prepared in your attire no matter when you go.
Our HAL cruise was May 31-June 7, 2009 and it was perfect weather! My friend went in 2008 about the same time and also had great weather. For our cruise it was in the mid 70s at Glacier Bay and clear. We had warm weather in every port and Juneau was very warm. The Ranger on board at Glacier Bay said they are more likely to see clear weather at the Bay in late May than any other time. I know weather in Alaska can be cold and rainy one week and great the next but you do have a good chance of great weather that May/June week--we did!
The reason why it's cheaper is b/c the weather is still "iffy" at that time of year. You may get more rain at that time of year compared to Mid-June and July. But you'll be fine. We've had great weather all summer. September is when the rain really starts coming down.
We did a 12nt cruisetour with Celebrity last year. Began on June 1st in Fairbanks, took the train to Denali then Talkeetna, then motorcoached to Anchorage then down to Seward. After 5 nts, we boarded the Millie on June 6th for the 7nt cruise. The weather was beautiful and warm most of the way down. Hit rain a couple of times but nothing bad. Got sunburned on our balcony at Hubbard Glacier, it was gorgeous!