We will be based in Copenhagen for a month in the winter. Will it be worth venturing out of Copenhagen or Zealand at that time of year?
Danes travel to Norway to ski -- langrend in Danish, langrenn in Norwegian.
Yes, yes, yes, yes. If you're going to be in Denmark for a month in winter and Christmas is during that time, you are in for a treat! The Danes do cozy and holiday sooo very well! And there's an excellent train system, so you can travel with ease. What are you interested in? Maybe we can make some recommendations!
You already plan to be there, so now plan to make the best of it and see as much as possible.
FYI, if you're considering a weekend in Stockholm, direct trains take 5 hours each way, and that's about as simple as winter transport can get; advance-discount tickets at www.sj.se. Flying to any neighboring capitol can also be quite affordable; see www.skyscanner.com.
Re-skiing. If you're game, try Åre in Sweden or Trysel in Norway. Trysel's probably marginally closer, but Åre is easy enough if you fly to Östersund and take the train from there.