What’s a horse got to do with it?
According to the editors at the OED, “horse-” was a common prefix for various plants indicating a “strong or coarse” variant.
I have read that some speculate that that derives from a bad translation of a German(ic) word “meer,” meaning “more.”
“Meer” was mistranslated as “mare” which then became “horse,” or something like that.
I don’t know how well that is believed or documented, though.
BTW, horses have callosities on their inner legs called “chestnuts,” but I don’t know why they are thus yclept.
In the case of “horse chestnut” that you mentioned, that seems to be different. The OED editors cited someone who said that they were used to treat horses’ coughs.
What’s a larch got to do with it? That’s a conifer softwood, and the horse chestnut is a deciduous hardwood, is it not?
I thought The Larch was number 1.