I too will be cruising to Alaska very soon and from what I have read and heard, yes for the had and gloves and unless you are going up to a glacier, you can get by with sweatshirts, t-shirts and layer the clothing as needed. Also some rain gear would be a good idea to pack and an unbrella too.
Do the layer thing as Donna suggests. You might also want to take a "wrinkle suit" ... those flannel-lined pants and jacket that come already wrinkled for your packing convenience. A hooded, lined anorak jacket would also be good.
Don't pack a lot of sweatshirts. Buy 'em as you go along, don't spill anything on them and you can give them to your friends and family when you return.
Also a poncho. They are great insulation! And they fold up really small. You can grab them for a few dollars at your local discount department store. Umbrella, yes.
I recommend "glitter gloves" which you can find at a ski or sporting goods store. Wear them under another pair of gloves. Plain cotton work gloves serve the purpose. The point of the glitter gloves is that you can still use your camera or binocs after removing the outer gloves.
Went on the Sun Princess this past July. It was fabulous! It will be cold by the glaciers. I took a Helly Hanson jacket (found online) - like a Gortex. It worked great! Also worked as a rain jacket - and there WILL be rain. Count on it.
Hat or earmuff or a headband type to cover the ears - especially if you like walking the promenade which was wonderful in Alaska.
Gloves - yes - something lite though - like runners wear.
Take a digital camera or else lots of film and ENJOY.
You will love your cruise.
Feel free to email me for any more info or to see my pics.
Sorry so late in responding. Layers and a waterproof windbreaker will get you through most anything. However, it really depends on your cool tolerance. I'm from Minnesota. It seemed that me and land-locked Canadians were constantly removing clothes because we were too warm. West Coasters and southern US folks were usually cold. The ship itself was warmer than I keep my house. The only time I wished for my "heavy" jacket was on the turn at the glacier. The rum enhanced coffee helped .