Elle, just tried under 'great guns' and found nothing, but I finally found the expression under 'gun', meaning simply doing something with vigour and efficiency.
We went through this before, comparing our various editions of the Brewers -
According to 'Idioms and their origin' it dates back from early 19th Century, when it referred to cannons as opposed to smaller portable arms; it then evolved into meaning a imposing /distinguish person (as opposed to lower classes I suppose), and then extended to a violent gales , as in 'it blows great guns' (canons roar, so do storms/gales. But in early 20th Century it only alluded to repeated firing of mighty cannon in battle.
No mention of horses at all.
Amazing how different two books of reference can be !