It really depends on your travel personality. I dont get cold easily, and we have been to Alaska several times now (all in May). We are going again this coming May. 🤣. In June, you may want a pair of shorts! We have had days in the 60s in May.
I always pack in a carry on only, and have no problem re-wearing things like jeans etc. I bring 1 sweatshirt, 1 thin jacket that I wear individually or together as needed. I am definitely "less is more" packer/traveler tho.
I would say you dont need a formal dress. Some folks do dress up, but overall Alaskan cruises are more on the casual side. I usually bring 1 pair of black pants for dinners and a few silk blouses. Sometimes I wear dark rinse jeans.
Ive never been cold on our cruises but it really depends on the person obviously. I bring items to layer, and if anything, Ive had to take off layers because I was warm. Also depends on your excursions. We bring single layer waterproof jackets (got then at Costco for $20) and theyve been great. Easy on/off, small to pack.
We wear sneakers...havent had problems with them getting super wet (even in rainy weather).
I bring gloves I wear for running because theyre small and easy to pack. But Ive never worn them. My husband has worn a knit hat on a few excursions...I never needed one myself. But those items are small, and its not a big deal if you dont use them.