Speaking from experience here, I've spent the last few days with a smoker in Mongolia, and he has been driving me insane, clucking for his next fix! A new law introduced last spring means that it is practically impossible to buy cigarettes in Ulaannbaatar. They can't be sold within 500m of a government owned building, school or university....which pretty much includes the whole city! To get your hands on a sneaky fag you need to head further afield, out into the countryside. If you're planning a ger camp stay, ask your driver to make a ciggie stop once you're out of the city centre. Otherwise it might be best to stock up on a few packets before you reach UB....or maybe it's a great place to give up all together!
If you're smoking in the city, you may be pestered into "saving twos" by a passing Mongolian. My other half reliably informs me he has yet to smoke a full cigarette in UB, and he always gives the last few drags to an equally desperate Mongolian smoker!