After we kill all the pinkertons, there are 2 lawmen coming to investigate. We get the "exciting horse" from one of these 2 lawmen.
The other 2 "exciting horses" we get early using the same way are Dark Bay Andalusian and Palomino Dapple American Standardbred. For those 2, you can buy them from different stables after Hosea's Hunting mission with the price of 150. For the Andalusian one, this is the earliest possible way so it is really precious, too and for That Standardbred, you can get it from other chance events, which decreases its value a little.
I don't think they are as special as this baby because this one is goodlooking to me and we get it really early. Although I will make videos of those 2, too.