Howdy,

first of all, I don't think every way needs the information whether horses are allowed.
Second: https://wiki.openstreetmap.org/wiki/Key:bicycle
The first sentence: LEGAL restrictions.
You can add the width and the smoothness and the MTB Scale to the way. It's up to the data consumer to interpret this information.

Same goes for horse
https://wiki.openstreetmap.org/wiki/Key:horse
It is a legal key. Please use it that way. The page links you to https://wiki.openstreetmap.org/wiki/Key:horse_scale. If you feel, you need to put the info for horses on the way, please use this.

That's what I think and what people put in the wiki.

cheers :)