I just fixed mounted combat for my games the other day. I was making the characters for my players, because they are new to 5e, and because I have been enjoying doing it. It got me obsessed with making sure that 1) everything the character can do is spelled-out rules-wise & 2) It all fits on one page (with not-small font!).
With that in mind, I was trying to fit the ranger's horse on (and then the fighter picked up one too, after defeating a villain mounted on a warhorse). So... two characters with horses. So I started with the whole warhorse monster statblock. I was tying to cram it into a corner, when it occurred to me that I could just move stuff to the PC. I left the mount's AC, HP, and Ability Scores in a little box and I moved its speed, charge, and hooves attacks under the PC's options. So it looked like this:
Speed: 30 ft. (Mounted) 60 ft.
Charge. (mounted) If you move at least 20 ft. straight toward a creature & hit them with your horse’s hooves, they must make a dc14 STR save or be knocked prone.
Actions:
Longsword +5 for 1d8+3 slashing damage.
Hooves (mounted) +6 for 2d6+4 bludgeoning damage.
etc.
So now the horses' attacks are just part of the PC's suite of features. And they'll actually use them. They "ready" those features by mounting their horse, the same way you ready your sword by drawing it.