It sounds to me like farmer Smith is calling upon the knacker!

Animals dying on farms was such a common occurance that a specialized job for it was a common occupation, even from the middle ages onward to the present day! The knacker (let's call him Cutter, cuz we've already named the farmer) would bring along his cart, load up the carcass (almost always whole, but I suppose he might be able to break it down a little bit into more manageable chunks if it was an especially large equine), and take it back to his residence, the knacker yard, for rendering into various products and raw materials. Cutter lives on the outskirts of town, partly because his job was considered very "dirty" and lower-class, but, more practically, because the techniques he used tended to be exceptionally smelly. It would ruin the pastoral aesthetic if you could smell tanning vats, crematoriums, and any decomposing animals the knacker hadn't got to yet.

No part of the horse went to waste! The meat could be used as feed at farms for various carnivorous animals like dogs, pigs, and foxes (note: meat from the knacker was NEVER used for human consumption); the hides could be sold to the local tanner for leather making if the knacker didn't already have the facilities on hand; the hooves could be processed into animal glue, which would be supplanted fully by the chemical glue we use nowadays until the 20th century; hell, even the bones were ground up and used as bone meal fertilizer!

Cutter had a difficult, smelly job, but it was an essential one. Animals died frequently at farms, and most weren't raised with human consumption in mind. It was also a very lonely one. Nobody liked the local knacker, and his uncleanliness of a job often led him to also take contract work as a locality's executioner. The job had a similar social stigma as the knacker, and it usually paid reasonably well. It became a very common occurance for the knacker and the executioner to be one and the same person, though I can only imagine the most introverted and misanthropic people could thrive in the dual postion...

I hope I answered your question! If you have any more, please leave me a comment!

Edit: a word here and there and correcting some punctuation.