Would it be an interesting idea for when you forage a clover on a horse, instead of the clover going into your inventory, having the pony power stamina increased by about 5-10%?
I understand Jorb's worries about how overpowered permanent horses could be, but this would be a finite way of temporarily increasing the duration of your horseback-foraging, that there is no way to really abuse or stockpile clovers for. The clovers would need to be picked fresh while on a horse, not fed from the inventory, so it would only be by chance while crossing grasslands that you would come across them and mildly boost the horses stamina.
I know there's been times where I've wished that bar would last just a little bit longer

Haven't put much thought into balance/percentages, but this seems like the best way to extend horse longevity outside of permanent taming (that I've thought of so far).