If you are not with a Mongolian national then under no circumstances should you get into a normal car acting as a taxi. It is fairly common for westerners to be driven out into the countryside, robbed and dumped. And if this happens between December and February you'll be stranded in -30C temperatures.

Apart from that I agree with deckman. Korean Air is the only civilised way to fly into Mongolia, and during the summer they have a daily service, even if the return back to ICN leaves and arrives at awful times of day.