We took our Alaskan cruise in August when it was 100+ degrees at home. We LOVED sitting in the hot tub, drinking a hot chocolate and watching the snow fall around us on deck! Royal Caribbean is a great cruise line in terms of plenty to do on board as well: Besides the great food, there were movies, live shows, gambling (at sea), lectures, crafts, dance classes, exercise equipment, a spa... This is a cruise where a cabin with a window is WORTH the money!
Royal Caribbean - Radiance of the Seas Alaska is recommended by wileymax