I should also add another use for the saddle horn: Saddle bags.
When we pack up and go camping, I often keep a bag over my horn and one behind my saddle for my stuff. There were times when I was younger I'd go out on my good old gelding and just spend a night in the woods, but I needed all my supplies first.
Horns serve many purposes, not just dragging cows.
Also, using as a handle, DEFINITELY better than the mane. When a colt decides they suddenly don't like you anymore, put their head between their knees and start bucking....It's REAL hard to get a hold of that mane! At our barn, we start everything in a western saddle with a stable horn, even back when we used to get a couple eventing prospects.
Plus, any horse can have a fit. Do what it takes to stay on. NO shame in using that tool when you get in a dangerous situation.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.