That is really interesting and results from your very careful observations. Most domestic animals aren't that good at self-medicating mainly because they haven't learnt the skills as youngsters either by themselves or from their peers AND haven't been exposed to a wide range of medicinal plants during those formative years. So quite often they can accidentally poison themselves. As you know, the strong medicines are also often toxic but I always reckon they should have access to a small number of these feared plants just incasee they need them but not enough to harm them. They kinda half remember what to do but havent refined the skills like they would in a natural situation surrounded by elders.
I've often heard of horses (and cattle) using willow when needing pain relief. Some people even offer their willow cuttings up to confined horses.

yes this horse was raised loose in a pasture in a herd situation from birth. I think that helped him learn about the plants.