Dothraki are mounted archers with re-curved bows. I believe they massively outnumber Westeros' army. They wouldn't charge the knights; they'd attempt to bury them under a mountain of arrows. Same way the Mongols beat the Poles. Where's it stated that Westeros bows have greater range?
I don't know if that would work on it's own. Westeros isn't flat grassland and they'd have to lay siege to cities. But if they arrive with Dany a lot of support for the Lannisters would crumble.
I've heard it mentioned in the show or book. First one obviously, not sure where. And even then if their ranges were of comparable range than it would be more than easy to fire off your arrows at them on approach. It doesn't matter. A well trained smaller army has often in history beaten a vastly more numerical foe. As a matter of fact there was a situation quite similar to the ones in game of thrones. A vast horde of lightly armed marauders like the Dothraki up against an army. 10 to 1 odds and the defenders won because they knew the land better, and utilized the terrain to their advantage to force them into attacking when they don't want to. I'm trying to remember the name. In REAL LIFE combat a scimitar is a joke of a weapon. There's a very good reason why the spear was the defacto armament of the time. Cheap to mass produce, and effective against cavalry and people with swords since you out range them. Swords were more specialized weapons that the rich usually used once it came to more close ranges of close combat. Even then slashing wasn't utilized so much as thrusting. I mean just look at the point of the sword. If it was meant for slashing it would be shaped like a scimitar or katana with a curved blade that cuts more when it slashes. Their weapon of choice in real life would do jack squat against any armored knight unless you got incredibly lucky to slash at his joints. Even then the curved sword will be meeting leather or chainmail or both! It cant focus enough force into that point. So why were scimitars used? Well they were made because they fit the condition of the people at that time. A lightweight weapon to be carried around for long periods of time in the desert. Often heavy army would be a liability in such terrain, thus it would be a more prudent choice since heavy plate armor wouldn't be as commonly encountered. Even then it was more often a ceremonial weapon.
Genghis Khan was so feared because he wasn't an idiot like Drogo and his herp derp army. He would regularly make use of new technology and adapt it into his army. He and his men used armor as well. Overall they were far more heavily armed than a lot of people realized. Khal Drogo and is dothraki raiders are a joke. Now if they get support, the whole thing changes. Then again what would you rather have. Dothraki with dragon and support from one of the seven kingdoms? Or Genghis Khan with the support of dragons and one of the seven kingdoms? Seems obvious to me.
Edit
When I mean armour, I mean light armour. As opposed to Dothraki and their suicidal use of no armour. Closer to the huns than anything.