I have to say that horses would be a big fancy stuff in early game but i have to disagree with you or mind things you dont mind
So
Horse would be vulnerable only if sleeping
(i have horse, this animal weight over 800 kilo and if it punch u even light you have very high risk of having broken bones so whateverhorse charge, it will be unstopable only by big horde)
Horses need to eat and drink too (you dont mentioned it)
Horses would eat vegetables and sometimes sugar you give them and just grass (its their main diet, but sometimes it is not enough)
Charge abality
Horse if running in fast speed when you have a crafted spear with knife or smt you can one tap zombies but it will reqire a high level of riding and good condition you and your horse.
As well devs can add a multiple horse bread that will give other effects
And finnally one more class that will be pointed at horses (horseman, medival battles reconstructor?)
I think its ebough