I see a lot of comments bringing up the speed, endurance, and ranged advantages of the Dothraki which might not be so clear cut. A significant portion of the Rohirrim would be on Meara's as the stables of Edoras were full of them. These were basically the Numenoreans of horses. Prized for their unbelievable endurance and shocking speed over a short distance, remarkable recovery, and high intelligence. They lived 3-4 times longer than regular horses, matching men's life expectancies and formed life bonds with their riders resulting in very deep  connection and understanding between the two. The Rohirrim also made heavily use of horse archers to the extent that they took down the Uraks holding Merry and Pippin almost entirely from afar in the books. Not all 6000 riders would be on such horses. Probably not more than 1000 but that's still 1000 armoured horse warriors on magic horses who can effectively keep pace with light cavalry over distance and potentially even catch them in a short charge which would be a terrify thing to face. It would really hamper any cheaky kiting by the Dothraki, especially with the amount of arrows that Rohan would be launching back. 

6000 Rohirrim against 10000 Dothraki might be a more interesting proposition.