Don't know much about the country but, in terms of geography, i choose Air Nation, since it's mountainous and plateau, high altitude i think. which can be "windy" but it could also be earthy, so, Earth Kingdom could be too

But definitely not Water tribe nor Fire Nation for me

Fire nation

What Mongolia are we talking about and how? Are we talking about the Mongol Empire or the geography of modern day Mongolia or the culture and traditions? These are so much more complicated and needs to be specified

The Mongolia here & now

Mongolia is very cold and has lots of snow. It also had many huns. I'm picking Water Tribe. On top of that, a lot if pepple wore white fur clothes

I think different cultural elements of Mongolia could be in different nations. For example, Air Nomads' cuisine based on milk, an expansionist leader in Earth Kingdom or Fire Nation, fur thick clothes and yurt in Water Tribes, nomadic hunters in the Earth Kingdom, falconry and archery in Fire Nation, tengri elements in Water Tribes and Air Nomads etc etc