Hi there Yvonne.
You won't see the best of Mongolia, but there are still things to be done if you can bear the cold (-30 to - 40 ish?). I've never been this time of year, but I know Gans used to organise winter activities for ex-pats working there. You can ask him kbgans@yahoo.com.
The Mongolians survive as do their animals (except when they have 'zuuds' - a thaw then a really deep freeze). How long are you in China for? Maybe it's an option to visit on your way back?
