According to Viserys (who is admittedly an idiot) in A Game of Thrones:
“We won’t need his whole khalasar,” Viserys said. His fingers toyed with the hilt of his borrowed blade, though Dany knew he had never used a sword in earnest. “Ten thousand, that would be enough, I could sweep the Seven Kingdoms with ten thousand Dothraki screamers. The realm will rise for its rightful king. Tyrell, Redwyne, Darry, Greyjoy, they have no more love for the Usurper than I do. The Dornishmen burn to avenge Elia and her children. And the smallfolk will be with us. They cry out for their king.”
Dany then has a conversation on the same subject with Jorah, who is not an idiot (except perhaps where women are concerned):
“Could the Dothraki truly conquer the Seven Kingdoms?”
Ser Jorah’s face grew thoughtful as their horses trod together down the godsway. “When I first went into exile, I looked at the Dothraki and saw half-naked barbarians, as wild as their horses. If you had asked me then, Princess, I should have told you that a thousand good knights would have no trouble putting to flight a hundred times as many Dothraki.”
“But if I asked you now?”
“Now,” the knight said, “I am less certain. They are better riders than any knight, utterly fearless, and their bows outrange ours. In the Seven Kingdoms, most archers fight on foot, from behind a shieldwall or a barricade of sharpened stakes. The Dothraki fire from horseback, charging or retreating, it makes no matter, they are full as deadly . . . and there are so many of them, my lady. Your lord husband alone counts forty thousand mounted warriors in his khalasar.”
“Is that truly so many?”
“Your brother Rhaegar brought as many men to the Trident,” Ser Jorah admitted, “but of that number, no more than a tenth were knights. The rest were archers, freeriders, and foot soldiers armed with spears and pikes. When Rhaegar fell, many threw down their weapons and fled the field. How long do you imagine such a rabble would stand against the charge of forty thousand screamers howling for blood? How well would boiled leather jerkins and mailed shirts protect them when the arrows fall like rain?”
“Not long,” she said, “not well.”
He nodded. “Mind you, Princess, if the lords of the Seven Kingdoms have the wit the gods gave a goose, it will never come to that. The riders have no taste for siegecraft. I doubt they could take even the weakest castle in the Seven Kingdoms, but if Robert Baratheon were fool enough to give them battle . . . ”
So the answer appears to be that the Dothraki can win on a battlefield, but not in a siege.
