The Dothraki aren't all that impressive as an army
Since season one, they've been talking up the Dothraki, saying no army could defeat them in the field, and now we have Jaime confirming that "they'll beat any army." For the life of me, I can't see what anyone in the show would be basing this on. It just goes to show how little the show's writers actually know about pre-gunpowder warfare. The only things I see the Dothraki have going for them are numbers, and ferocity. They don't wear armor, so they'd absolutely get slaughtered by armored heavy cavalry in any melee. They don't use lances that I've observed, so their impact in the charge would not be all that great. We've seen a few archers among them, but nothing that would make them look comparable to the Mongols of Genghis Khan, who were primarily horse archers and the greatest light cavalry of their day, who would use their mobility to shoot and move, shoot and move, and avoid contact until their archery had opened up gaps in the enemy's formations they could then exploit.
The Dothraki just charge in, the few archers among them shooting a couple of arrows here and there, and most swinging those curved swords of theirs that appear modeled on the ancient Egyptian Kopis -- a weapon which, as Matt Easton of scholagladiatoria pointed out, is actually not a bad sword for infantry, but it's not at all a good cavalry sword.
In short, I can't see anything about the Dothraki that looks all that impressive from a military point of view. I can say with complete confidence that they would be totally unable to break pike formations like the Scots used against the English at Bannockburn, or which Swiss mercenaries and German Landsknechts used on the continent in the late middle ages/early Renaissance. I see nothing about their tactics, weapons, or equipment that would enable them to do it.
I know it would have added a bit to the expense of the show, but the creators should have given them a little armor, made most of them archers, and show them using tactics more like the Mongols.