The Fairmont Banff Springs is a stunning hotel. It's definitely worth a visit to wander the grounds, inside and out, especially with snow. They also have a fantastic spa, and I would highly recommend an afternoon with a spa treatment. This gives you access to the common area that has multiple different waterfall pools, a mineral pool, a hot tub, and steam and sauna rooms. One of the restaurants would probably be nice for a romantic dinner.
You can also do an ice walk in Johnston Canyon, which I think would be amazing. The canyon and it's waterfalls are beautiful. I think seeing it all frozen would be a very unique experience.