Spoilers ahead ******************* Do you think Daenerys would have conquered Westeros with Khal Drogo? I don't think she would've as places like the Vale, The North and The Iron Isles would have inflicted heavy losses against the Dothraki. They would probably mutiny against their Khal and get defeated. What do you think?
So far it seems everyone agrees that the Dothraki would fail miserably in Westeros. When you consider the skilled military leaders like Stannis and Tywin it seems more unlikely the Iron Throne would fall.
The dothraki are vast in numbers and are skilled warriors. However, like you stated, the Vale would be incredibly difficult for them I think. They are horse lords, not sure how they'd fair against the Iron Isles either. I voted no.
They would win, because Daenerys would use her dragons, besides - the Dothraki are very skillful horsemen, just like Mongols, note that Genghis Khan managed to conquer some of the largest empires in the history (China, Russia, Persia) - all of them had heavily armored capitals, with large armies guarding them. Basically, it's all about tactics and strategy.
The North is waaaaaaay too cold for them, they'd be screwed up there. The Vale... well, yeah. They probably wouldn't do well against the Ironborn either, seeing as they don't trust the sea and all that.
Besides that, yeah they would probably make quite the impact on the Reach / almost everything below the Neck :)