Just a few links to follow up on the question of medieval Catholic horse consumption:
8th century - Catholic backlash against eating horses as Catholicism spreads (through Carolingian conquest and missionary activity) into northern Germanic areas, where horsemeat had important ritual and cultural functions.
Pope Gregory III's letter to Boniface (732):
"You say, among other things, that some eat wild horses and many eat tame horses. By no means allow this to happen in future, but suppress it in every possible way with the help of Christ and impose a suitable penance upon offenders. It is a filthy and abominable custom."
A sort of correlation can be found in Iceland, the last outpost of Germanic paganism. Here is an excerpt from Njalssaga (which is amazing and everyone should read anyway). It was written sometime in the late 13th century, though it is set in the early 11th century at the time of Iceland's conversion.
"Our first principle of law is that all Icelanders shall henceforth be Christian. We shall believe in one God -- Father, Son, and Holy Ghost. We shall renounce the worship of idols. We shall no longer expose unwanted children. We shall no longer eat horsemeat. Anyone who does these things openly shall be punished with outlawry, but no punishment will follow if they are done in private."
Within a few years these heathen practices were prohibited in private as well as in public.
I didn't pull it up here, but there is similar evidence that pagan Ireland assigned a ritual function to horsemeat (and some other unsavories, like dogmeat) which further led to the eradication of these practices over the course of the conversion (5th-6th centuries).
For some more general surveys, here we have a reasonably well-researched blog post about the formation of a horsemeat taboo in Anglo-Saxon England: http://www.medievalists.net/2013/02/20/why-did-the-english-people-stop-eating-horses-in-the-middle-ages/
...and this blog post on Western Europe's relationship with horsemeat, from pagan prevalence to Roman and Christian aversion to a 19th century revival: http://leslefts.blogspot.com/2013/12/killing-pegasus-history-of-horse-meat.html
Note that high medieval sources on the prohibition seem lacking - possibly the taboo was simply edified and beyond remarking at this point. The mentions of eating horse-meat as a last resort during sieges and famines in the 15th century suggest something similar - horses, like dogs or cats, had become beasts that Europeans proverbially did not eat under normal circumstances.