I want to see the city but do get cold, so walking around for hours may not be a good option. I'd appreciate any advice on other ways to get around and the best indoor activities, including museums and shopping areas. I do plan to go to Scansen and the Abba museum and some history museums, as well. We are staying at the Grand Hotel.
I visit a great number of museums , and on a visit to Stockholm , this one was a hidden gem - https://www.thielskagalleriet.se/en/
If you go to Skansen, go on the weekend during the Christmas Market. Otherwise, I’d suggest skipping it.
As far as getting around, I’d suggest getting an SL travel card for the duration of your trip and rely on the bus or underground (tunnelbana). You can buy either a 72 hour card or a seven day card.
The Abba Museum doesn’t take cash, so make sure you bring a card with you. I would recommend that you include the City Hall and the Vasa Museum in your plans.
With regard to shopping, the two big department stores are NK (https://www.nk.se/stockholm/in-english/ ) and Åhlens. There is an underground pedestrian walkway that runs from T-Centralen past both of these stores and up to Kungsträdsgården. NK has decorated windows during the Christmas season.
I think most tourists like the various little shops in Gamla Stan. There are also lots of trendy shops on Södermalm.
As Laura says, buses and the subway (T-bana) will take you where you need to go, although for getting around within a neighborhood (like Gamla Stan or Sodermalm), you'll need to walk. Just bundle up. Taxis are available as well, but are VERY expensive, so unless you're with a group or splurging, you'll want to minimize your use of them.
Have you looked at Rick's Scandinavia or Snapshot Stockholm books? While they are geared to a summer visit, he does cover a number of indoor attractions like museums. Even though it's outdoors, the Millesgarden (a sculpture garden with great views) was a real highlight for me, as was the Vasa and the National Museum.