Do you know what the accident was? Any chance he hit his head and maybe his eyes are now failing as a result?
Also, horses do not have depth perception.
They see that dark in the mud puddle as a big black never ending hole that is going to eat their legs up.
Some horses are more concerned with that, than others. Just like some people are more afraid of the dark than others.
I have a horse that knows, without question sixteen boogie men are coming out of that dark water-filled spot in the road, yet I can hardly hold him back when we get to the lake because he loves to swim. Go figure
Between being born not having depth perception and the accident from years ago, your horse has decided water puddles are not in his Happy column.
As far as training him - he's going to have to develop more trust in you than in his Flight Instincts.
I've had horses jump over the puddle, until I found one in the woods there was no getting around. I was fortunate to have a well seasoned, no-fear horse with us. That horse went calmly thru first. I had to do a lot of convincing (I did not get off, it was too muddy, he's 16.1H, I am 5'2" - lol lol) but I finally got him thru.
I made him go back and forth until he settled down and realized the puddle wasn't going to eat him alive.
After that, the only thing that seems to keep the fear from creeping back, is to make a habit of riding thru the puddles every chance you get<---the wet saddle blanket theory
Hope this helps