You cannot walk on the Glacier if that is what you are thinking of doing. You just look at it and take pictures. The only way to do that is to take a helicopter excursion. If you are on one of these then I they provide special boots to walk on the glacier........also think they provide warm jackets but I'm not sure.
You will not need a heavy coat in Alaska, but a warm jacket and warm/heavy sweater will do. You should layer your clothes.
When I went this past May it was very cold and windy and I needed my winter jacket, heavy sweater, turtle neck t-shirt, hat and gloves/mitts. When I went in June and end of August, it was cold in the morning but warmer in the afternoon, so I was "peeling".
There are several great hiking trails there that are very easy to walk, no special equipment is required. Everything is well marked so you won't get lost. There are lots of shuttles from the ship that run every 20-30 minutes, no need to book with the cruiseline, its way cheaper on your own. Make lots of noise while walking so you don't sneek up on any of the bears. (make sure you can outrun at least one person that is with you and you will be fine )
I went at the end of August,,just layer. I went anyhwere form just a long sleeve shirt, to a sweater and jacket but not a heavy snow jakcet,,I live in S. Calif and we don't own those kinds of clothes.
I took a helicopter Glacier walk. They give you these funny boots so you don't slip on the ice, some heavier jackets and an orange safety vest so you can be spotted if you slide off into the ocean (okay the ocean part was fake but you get the idea). The vest was really a life preserver as required to fly over water.
HAL Volendam 2004
HAL Maasdam 2006
HAL Zuiderdam 2007
HAL Eurodam 2008
CCL Paradise upcoming 2010