Bronn can't wear armor? He can, just like any other man. He's a lord now, and has been a knight before that. The only reason he didn't wear it in his duel against Vardis Egen was because he was dirt poor and didn't have any.
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As for Dothraki vs Westeros. I think even in an open field Dothraki don't have much of a chance. They could scare and slaughter the regular peasant levies, but I don't see them standing up to heavy cavalry charges, or top notch spearmen like the Dornishmen.
Beyond the technological advantage, Westeros also has quite a few good military commanders, whereas the notions of strategy and tactics seem alien to the Dothraki. They're good at raiding, not organized battles. See that story about a 20 thousand Khalasar charging into a wall of 3 thousand Unsullied spears over and over again(18 times) untill half the Khalasar was gone.
I'd say even a considerably smaller Westeros army could have given that work to Drogo's army if it was led by someone like Stannis, Randyll Tarly or Robb Stark.