the kenghis kahn is a 5 star,the ulan batar is the old 5 starwhich is really like a 3 star but thwe food is very good , go to the museum of natural history there to see the dinosaur bones and eggs aand to to the museum of culture to see the costumes that the tribes wore over the history, go to the big yurt tent for a local dinner

There are also some cheaper backpackers places which are fine if you pay for all the beds in the room, so you'll have a single room.
Go and find Dave at the English pub next to the opera building on Sukhbataar Square, he should be open and can add more tips on what to do although the museums are good as shoe said.
Ulan Bataar does not have massive snowfall, it's too cold, you'll find the ground is covered in ice for the most part, but by all accounts it's an interesting time to visit, I've only been there in the summer.
There's also quite a good Belgian cafe on the main street with a balcony a little raised up from the street which is a good place to watch the locals going to and fro.
If you see Dave, say hi from me, he might remember. I was thinking of getting an apartment there, tourism will take off eventually, even though the city is pretty dirty with rubbish.
Lovely exotic girls by the way, different from any other culture with their rosy cheeks, a little like Tibetan maybe.