Is this going to become a trend? These "What if pony" questions should really be in ponythread...

The Mongols will probably kill plenty of ponies in the first few engagements, but in the long run they will be cremated. Pegasi controlling weather means they can make storms wherever the Mongols are (lightning and high winds, the lightning kills people, the wind makes their bows useless). Drop some tornadoes down in the middle of their ranks and put snow in front of them to slow their advance, and retract your own population to Canterlot (which is wonderfully situated on the side of a cliff).

I would go so far as to say that even guns aren't going to work well in Equestria, much less horse-archers. Remember, the Nazi's were stalled by winter in modern times. The wreckage of an invading medieval would be total and complete.