The good news is, that is definitely not a mountain lion. Their scream is a very distinct sound. So are their growls and hisses, for that matter. Even if it were a cat (and it sounds like a bird), it would be a small one. Mountain lions are decent-sized animals and don't make small, tinny sounds like that. They do purr, but you obviously wouldn't hear that unless you were quite close.
It sounds like a peacock to me. Peacocks can make a wide range of sounds, including a truly bizarre one that sounds like a door buzzer. Their "voices" can also vary a bit from bird to bird, as I found when I chose a barn with several dozen peacocks in residence (not intentionally; they're squatters). I suppose it could also be a fox but I have less experience with their sounds. I've lived near mountain lions and peacocks but not foxes.
Since you are nervous and anticipating a mountain lion when you head that direction, I wouldn't be surprised if the horse is picking up your alarm. It is unlikely that a mountain lion would hang out in the same spot without a kill or a den, which would mean plenty of evidence of its presence. The horse doesn't know where the track was found, but you do.
They're not bad, anyway. They live all over in California and with all of the urban sprawl we run into them (and bears, but that's beside the point). Every now and then a young or injured animal tries out going after joggers or bikers out of desperation but for the most part they keep to themselves. I used to see and hear them around my house before I moved. It was not a set territory for any one animal so they would pass through. I once scared off a young one loitering behind my house by flinging open the slider and hollering at him. You'd have thought I was after him by the way he took off.