I think a horse ambulance may be the next thing. After the two Model T Fords that are coming along slowly.
That is an ambulance for horses not a horse drawn ambulance.
I have found details for a couple, a Commer Car(later to become Commer) and a Thornycroft with an ingenious system for loading and unloading horses.
The cast wheels may do for both, especially if no one looks too closely.