[captain_dave]

During the Napoleonic wars the French cavalry called the bed roll bag that fit behind the saddle a portmanteau. To me that's a saddlebag.

[the OlLine Rebel]

That was a blanket I believe. Just as foot soldiers slung them around their shoulders.

In any case, as a person who knows something about horsemanship as well as mil history, I’ve never known saddle bag to mean anything but a symmetrical conveyance placed across the horse’s back or withers.