How complex does making a horse run cycle transition need to be

I could be mistaken, but in the video you showed us, it appears that the horse running animation is a single animation track played in different speeds. If that is the case, increasing the speed of the animation dynamically seems to be the way to go.
There have been topics with solutions discussing the speeding up of animations.
This might be of assistance:

Edit: Concerning the animation cycle transition itself, “AdjustWeight()” seems to be what you’re looking for. If that’s what you need, this might be of assistance: