Take a variety of clothes. It can very wet and could be cold especially if you venture on to glaciers. I would be surprised if it snowed. It is rather like Scotland with dramatic changes in weather. It's a beautiful part of the world - I worked there some years ago.
Sorry I can't speak for Alaska, but we crusied to Svalbard (Spitzbergen) at the beginning of June and while we were very lucky with the weather (no rain in 18 days)it snowed a bit twice and temperatures were on or around freezing, the lowest was -3. Windproof clothing is quite important because with a ship moving and wind chill it can be quite cold on deck.
How much daylight will you have in September? Please review your cruise when you get back. Alaska is on our list of places to visit.
Have a lovely time.
My advice is to dress in layers, when I did Alaska it was in September and the weather changed by the hour. The day can start quite cold but it can be warm when the sun comes out, but if it is wet it is usually cold as well.Enjoy your cruise Alaska is fantastic.
Hope you had a good time. For anyone else who is going. Layers. I have one of these interactive coats which are waterproof that you can zip a fleece in. When it was coldest I wore t shirt, fleece as well as the coat with the fleece zipped inside it. Take tights for under your jeans. I took denim jeans but a fellow traveller took cords which she said were warmer. Hat gloves, sunglasses a must. But it can get quite warm too. We spent lots on excursions which we do not regret one bit. The Captains choice wildlife quest in Sitka was truly amazing -saw whales close by (my dream)-wonderful guides. Take the ships travel pills if you get queasy. Also the pilots choice helicopter ride in Juneau-we landed on 2 glaciers! Not to be missed. I am so envious, would do it again tomorrow if I had the money.
Don't overpack though. We did Alaska in late Sept and took thermaols and all kinds, didn't need them. The weather was mild and even very warm on some days. Take a fleece and waterproof jacket and you will be fine - wouldn't recommend jeans as when they get wet (if it rains) they stay wet. Lake District has some really great lightweight (but lined) trousers that have seen me through Alaska, Norway, & Lapland in mid winter - whats more they are smartly cut so look good and work a treat to keep rain and wnd out.