The term “horse pistol” comes from the 17th and 18th century practice of mounted troops carrying the large pistols in buckets on the saddle, as a way of distinguishing them from smaller pistols that were carried on one’s person like scuppets and dags. It first shows up in writing about 1695, and in print about 5 years later.I have heard people comment on it but have never seen it in writing about "horse pistols" or larger calibers being for the specific purpose of stopping a horse. Though it does make sense.
Jay