Tattoos are not problems in Mongolia everywhere. As I observe, the young generation are very open-minded on tattoos.
In communist era, people used to see the people not well who had tattoos but now it is definitely different. Anyone can make it on his/her body. Nobody can judge it.
If you have tattoos and worry about living in UB because of your tattoos, please stop it!
As I see, the art of tattoos is already started to develop in Mongolia.
So, show your tattoos and enjoy it.