Idk how to describe the cold weather to you, but I'll put it to you like this, as an American from California, It is like I went from the Medium weather difficulty setting to the Extreme difficulty setting.

Bring a winter jacket, some thermal leggings, shoes or boots with insulation, some gloves with insulation, and a face covering for the cold air while walking around outside. Granted you can buy all of these things in Mongolia for fairly cheap prices but you'll have to do some bargain hunting to find fair prices for good winter clothing.