Hi there,
I moved to UB a week ago and I am really "impressed" about the air pollution (although I knew about it before...). Thus, I wanted to ask those of you who are familiar with it for a while what you are doing to keep your lungs working:-).
We spend the winter somewhere else! 
Ok, kidding aside (we do spend part of the winter in the US for holidays but still experience some of the winter), you do want to find a way to better seal your windows and get a HEPA air filter for your apartment (I remember getting my small one at Hermes center for somewhere under 200,000 tugriks last winter). It does help some, though on bad days you can still smell the smoke from outside. As for going outside, for all but the worst days I usually just make do with my scarf covering my nose and mouth. We brought masks from the US so I never looked for any to buy, but I'm sure there are a number of places to buy them in UB (pharmacies perhaps?). Best times to go outside are from late morning to mid-afternoon, between the morning smoke and the late afternoon when people start firing up their stoves again en-masse for dinner. It also depends on what part of town you're in... we used to live near Tengis Theater and the smoke was usually pretty bad, but as I'd walk closer to Peace Avenue or Sukhbaatar Square it was amazing at what a difference there was, and further over in Zaisan it is even better still.Â
So to sum up: indoors, get a HEPA air filter and seal up windows and doors best you can... outdoors, find a mask and wear a scarf over it and walk outdoors only in the early afternoon if at all possible.