
Yes, Dr.

I finally figured out how they do that. I was watching the final battle scene in "My Name Is Nobody" and it hit me. So I re-watched that scene in "Blazing Saddles," and, yep, same thing.
The rider yanks on the reins on the one side and simultaneously leans to the other side. For some reason this appears to cause the horse to lose its balance and fall in the direction the rider is leaning.
In "Blazing Saddles," watch in slo-mo and you can see the rider run his hand WAY up on the right rein as Mongo is drawing back to throw the punch. Then he jerks the snot out of the rein as the punch is thrown, and basically tries to fall off on the opposite side.
In "My Name Is Nobody," Henry Fonda was shooting the dynamite the riders of The Wild Bunch were carrying in their saddlebags. All the riders to either side of the explosion (from the camera's perspective) used this trick to make their horses fall way from the explosion. And they used Yakima Canut's Running-W trip on the ones that were between the explosion and the camera, so they fell directly away from the blast and toward the camera.