Horses are natural born swimmers. The size of their chest and lungs give them a significant bouancy aid. But bogs are not included.
I have swum on horse back whilst sitting in the saddle in a lake and in the sea - that's where the waves come in. No problems.
The horses were swimming along and me, well I was up in the saddle as though on a canoe.
The horse's hooves make a naturally shaped paddle and a horse can swim for hours - it is the temperature of the water that makes the difference. Be careful of very cold water.
But bogs - oh be careful. We have moors in Britain and they can be fun to ride. But if you are mounted on a local horse then they know what to be careful of and bogs are such things. If the terrain is boggy then let the horse choose the way and listen to it.
I won't ever take my own horse across to the moors where the bogs are. She would not know the way out.
Two of the memorable moments in my life with horses are associated with bogs. In both cases the horses went down into the bogs to their knees with me still mounted. To get off or not to get off - that was the question.
I am still here so we - that's the horses (William & Puddy) and me -, must have made the right decisions.
And by the look of those photos - so did you make the right decisions. Well done.
Give that horse of yours a special treat.
PS Get those signposts changed.