Yes, The same horses were used in the 7TH, the Cowboys, and the Indians sets. They came with a separate saddle, that had reins attached to it. The reins slipped into the horse's mouth, while the saddle was held in place by the rider. The horses have two holes in their sides to accept the pegs on the riders legs.
There are 2 poses and they came only in gray.
You can see copies in cheap Cowboys and Indians bag sets from Dollar stores. Some copies are actually pretty good and very close in size to the originals. Usually, they are in white plastic, but I've seen a very nice red-brown color, that is not common.
I would bet that you've seen these dozens of times and just didn't know what they were.
https://www.picclickimg.com/d/w1600/pict/162615569688_/Collection-of-1970s-Airfix-4-horses.jpg