Don't fly until the after the New Year so will be ringing in 2019 in icy Ulanbaator. When it's -31 and smoky out the idea of standing around Sukhbaatar Square for fireworks seems more of an ordeal than a pleasure. Still, that is apparently what people want to do: dinner followed by standing in the cold
A bit of a quirk here that I have mentioned; the first of EVERY month is no booze allowed, so I'm not sure much will happen after midnight.
Staying in sounds like the better option the more I think about it.