Those are great choices! I'm assuming you don't ski, otherwise you would have planned that already. Other options - you could go tubing and/or on a snowshoe tour at the ski resort or you could go cross country skiing - there are quite a few trails in the area.
I'd suggest leaving some time simply to walk part way along the lake and enjoy the beauty. Then use the rest of the day for snowshoeing/xc skiing/ice skating/dog sled rides.
There's only one company that operates dog sled rides in Lake Louise. Since there's usually a limit of 2 adults per sled, you'll probably need to book 3 sleds, which could get pricey. Also you'd need to see if there is still availability - could be a very popular day since it's the Saturday right before Christmas.
I agree that doing one of the snowshoe tours at Lake Louise or Sunshine could be a lot of fun. They offer excellent views - far better than those on the valley bottom trails where you can safely snowshoe in the Lake Louise/Banff area. Plus you have the expertise/knowledge of the guide. You can rent the equipment at the ski hills, and they may offer a discount as part of the tour.
Take a look at Great Divide Nature Interpretation's snowshoe tours. These folks are award-winning guides and they provide a great experience.