I prefer to study archaeological finds for historical evidence than T.V programmes which invariably contain poetic licence. Maybe the person who posted the pictures should visit Inner Mongolia and speak to some of the few 'Mongols' who live there to find out just how 'Mongol' it is. It isn't but it is very Chinese and if you look further you will find that Chingis Khan is being claimed as Chinese by means of extremely spurious argument.
The Mongols did indeed use a variation of mount, as I have argued myself. Not all were ponies by todays classification which is 14.2 HH, the Akhal-Teke is around 15.2 HH but none were as large as the Destrier which this rendition is. I can not think of a horse that size in any area that was subjugated at that time,
ie Batu's invasion

......Orda