Third week in May they had a blizzard in Tok and Valdez last year. Tok CG opened 4 days before we got there and that was because the water had finally thawed. When we got to Valdez June 1, there was 3" of ice over half the CG and we backed up to 4' snow piles in the places that were clear. Last year was cold, late, but there's no way to tell. About 5-6 years ago we had an acquaintance that was stuck in Yukon for two weeks in a blizzard in mid May.
I'm not trying to be a wet blanket here, but just be aware that things up north can be extremely variable. CG folks are usually on site or close even if they are not "open". A good list of phone numbers would be well worth your trouble. We've been up early and later in 06, 07, 09, 11, and 13.