My husband and I took the Transiberian Railway as honeymoon trip this May. We stoped in Mongolia for only 4 days and contacted Keith for a 3 night ger stay and 1 night in Ulan Bator.
Everything worked as planned: we were picked up at the train station by Davaa (who spoke very good English) and were driven (along with another couple) to the ger in the beatiful countryside outside the city, where we were kindly hosted by Yadmaa and Davasuren.
We had a full ger for our own, with 4 single beds, drawers, a little table and chairs, a small sink and a nice stove that kept us warm during the nights (even too much!). Yadmaa lit the stove every morning in case it went out during the night, so we could wake up war every morning. Davasuren prepared very nice authentic mongolian food. Very filling!
We took a horse day trip around the national park. We encourage everyone to try it, even if you're a horse riding begginer (as we were), as you can really enjoy amazing landscapes you might not see otherwise. Plus, the horses are really nice and you might even get the company of one of the dogs.
Appart from this, we had a lot of free time to explore the surroundings, learn how to milk a cow and just relax.
I believe this is as authentic as it can get in Mongolia, as this is really not touristy. Keith is really involved in the community and commited to its development. He also organises longer tours by horse around the country, but we didn't have time to try them.
As for Ulan Bator, you really enjoy the shower when you get there! There's not much to see, but Davaa and Nara were great guides, very flexible, and really caring.
We truly reccomend Stone Horse Mongolia if you're planning to stop in the country during your Transiberian, or any time! If you can, go between june and september, it will be less cold and greener. You can probably enjoy it any time, though.