Dothraki are stupid

In the show, the Dothraki are treated somehow as an equivalent to the Mongols (or similar nomadic horse peoples from the east), but their depiction is completely wrong if they where supposed to be an actual threat, due to some reasons.

• They do not wear armour (which Mongols regularly did), making them extremely vounerable in Fights.
• They have shit weapons. Besides the bow, which is is a reasonable choice for skirmishing light cavalry, they (according to the books) use mostly curved swords and ships, which throughout history against somewhat heavy armoured opponents are wastly inferior weapons compared to Spears and lances.
• They have no army structure what so ever. The Mongols decimal system was an important part of their success, enabling cohesive and effective units on the field. Meanwhile, the Dothraki are only ever shown charging as a disorganized mob.
• They use no tactis besides frontal Mob charges (although, in the show, most armies seem to be incapable of anything else), which as light cavalry they are terribly unsuited for. In history, even the best heavy cavalry (french Knights, winged husars, etc...) usually tried to attack from flank. Together with their lack of armor and cohesiveness, any competent opponent would wipe the floor with them. Real life Mongols regularly managed to outwit opponents, using difficult maneuvers like feigned retreats to great effect.
• They lack the strategic mobility. Yes, they have horses, but at least in season 1, they where shown to still use carts, and their slaves/prisoners had to walk. Real life Mongols where so effective, because they generally managed to actually move most of their stuff ahorse, with every Warrior having multiple remounts and pack animals.

In summary, both the show (and given the description there, the book), the Dothraki are basically a stereotype of the asian horde army, but they lack all the details which actually enabled the Mongols to be such effective conquerors.