Only tested on 1.15, but likely works on older.

Commands:

HORSEFALL toggle
horsefall.toggle
Toggles whether or not horse fall damage is enabled for you

HORSEFALL status
Shows status. No permission, because what is shows is dependent on your perms. I.E. needs horsefall.toggle to see personal fall damage status and horsefall.admin for the rest.

HORSEFALL protect-wild
horsefall.admin
Toggles whether or not wild horses are protected

HORSEFALL protect-riderless
horsefall.admin
Toggles whether or not riderless, tamed horses are protected

Config is straight forward. There is a bool value "defaultstatus". That determines what the status is for people who never chose a status. So a player who never did toggle has no value in players, so when their horse falls defaultstatus decides if they are protected or not. Set it to true to protect people by default.

In retrospect, I should have also made a permission node for that. Maybe like if defaultstatus is true and they have horsefall.useable or something. If you need that, comment in the discussion tab and I'll add it.