Mongolian Immigration Office said ''As long as you have got a valid visa, no problem" when I recently called them. But I haven't really heard tourists crossing over there. And the woman I asked didn't really reply when I asked since when it has been possible. I'll let you know after I talk to them again.
Cheers, Gana

Thanks for the help, but the problem is that no matter what the Mongolians say, you've also got to worry about whether the Russians will let you through. I don't know about Mongolia, but I know that Russia has some border posts which cannot be used by foreigners.