I’m in Arizona. I had a mare raised here - Arabian - who had no problem with mud puddles in her corral...but in the wild? She was 100% certain a wild mud puddle was instant death!
She had speed too. I also have a BLM mustang pony. His main limit on speed is being 13.0 hands tall - and now in his upper 20s - but I’d swear he can live on air, has perfect feet and...yeah...he can move when he wants.
We had several horses when I was a youngster. Almost all of them would pause & walk around a little tiny puddle of water on the macadam outside their paddocks. I figured it was because such puddles weren’t usually there, given we were in a pretty dry area.
I also remember a horse losing the Kentucky Derby, as it tried to jump the shadow of the twin spires right at the finish. It was neck & neck with another & that little hop caused it to lose by just a fraction of a second.