If the Dothraki are based on the Mongols, one thing to bear in mind are the Mongols' success in Europe. The Europeans assumed that the Mongols' arrows would have little to no effect. They were wrong.
The Mongols used recurve bows that allowed them to add tons more pull weight without elongating the bow. They would ride right up against the European knights and shoot right into them. Arrows went straight through.
The Europeans quickly scattered.
Something to think about.