It's an awesome experience to sit in the hot springs at night while snow is falling. However, I do recommend bringing a flashlight as they have no lights on the rocky walkway down to the springs. And be prepared to be cold once you get out!
Ski Haus is always one of my first stops in Steamboat. I always rent demo skis there; the equipment is kept in great condition and the edges are always sharp. The staff is helpful and friendly. They have really great merchandise; I almost always come out with a new hat or capilene or whatever I need that winter.
If you want a break from skiing or snowboarding in the winter, spending an afternoon snowmobiling is great fun! I have snowmobiled twice with Steamboat Snowmobile Tours, and have had two awesome experiences. The scenery is gorgeous and the ride is thrilling. It is slightly pricy, but well worth it. Highly recommended.
I always get the cutest hats at Moose Mountain. They used to have great iron signs on the back wall, but I didn't see any the last time I was in. They also have a large selection of Vera Bradley bags, and of course, cute moose themed items.
Their bloody marys are the best way to refresh after a couple hours on the slopes. The nachos are amazing, but bring an appetite because they are huge. It does get crowded, so there may be a wait for tables or slow service.