Most likely long pants and shirts. The key here is: layers and more layers. And don't forget hat and mittens - it gets cold on deck with the wind chill. We did Alaska in August and the weather was unusually nice - I wore shorts 1 day for about 5 hours.
My last Alaska cruise was in June and people were outside in bikinis by the pool and actually swimming in it! Since I'm a South Floridian I thought they were nuts. However, on that same cruise I wore a long sleeved shirt into Ketchikan and thought I would die of the heat. So, while you're around the ice (Glacier Bay, Hubbard Glacier, College Fjord and some shore excursions) it will be cold, you should take some summer stuff just to be safe.
Alaska's weather can change with a moment's notice. The last time I was there was last June. All but one day (in port) we had to layer our clothes to stay warm. The days that we were viewing the glaciers, we needed hats, gloves, scarves, heavy coats. One of my tricks is to wear silk "longjohns". I am very cold-natured, but hate to wear alot of bulky clothes. It's no fun to end up lugging around a heavy coat if the temp warms up. So, I usually opt for the longjohn top, a pullover thin sweater & a waterproof/wind -resistant jacket or sweatshirt for days in port. If you are going whale watching - be sure to dress warmly. Alaska is my favorite destination! Have a ball!!