a jian or dao would be appropriate, which would probably translate into the longsword and 9 ring broadsword. Later era mongols used scimitar esque weapons.
A big element is that they were so effective because the grew up shooting arrows at animals and just turned that into people for war. Every mongol was a skilled archer compared to the rest of the world. So even the heavy cav troops still need to have extra talent in archery.
The most complex part of trying to match it up is they used small hardy horses... not great big chargers... When you read the notes from their invasion of russia they were amazed by the size of the monstrous horses the russians rode. They preferred the smaller horses due to speed and maneuverability... which none of that really equates into pathfinder stats...