I've done it here in the Sierra Nevada, where the Sierra Club maintains about half a dozen cabins you can ski or snowshoe to. There's usually a downstairs with benches and tables and a counter (no running water, but lakes or streams are usually near), and an upstairs with mattresses (but no bedding). We bring stoves, food and sleeping bags. Usually there's a pellet or wood stove for heat, too.

I prefer camping out in the snow, but the huts are nice for an occasional change of pace. No comparison with a hotel - much more rustic, and some of them are fairly remote.

Here's a link to one:

Ostrander Hut

My understanding of the huts in the White Mountains and in Europe is that they often have caretakers, serve food, and are a bit more like hotels.