Re horses on the towpath. They duck their heads and go under the bridge at the edge of the towpath. Bear in mind that the horses used were mainly what we would probably call ponies or cobs nowadays - short-legged, sturdy creatures probably about 14 hands high. Larger horses pulling heavier boats would only be used on canals where they could 'fit'.
And fitting under the bridge would normally be no problem; even a 15 hand horse is only 5ft tall at its highest point (the wither) and horses used on the waterways were never harnessed with bearing reins and the like, which force it to keep its head high (you've all read Black Beauty, I hope!). A few inches clearance would be fine - just enough for peak of the horse-collar to clear, and a couple more for luck.
Also bear in mind that the horse could likely manoeuvre itself under most bridges in a relaxed sort of way, as the momentum of the boat would keep it going sufficiently to be steered through the bridge while the horse walked through without having to actually pull on anything at all, it could take up the strain again when out of the bridge.
Confession time. As a child I was brought up about 100 yards away from what was then a semi-derelict canal. I used to ride my pony along the towpaths for mile after mile, rarely if ever coming across anyone who even tried to tell me off for doing so.
My pony was around 13.2 hands and I rarely had to get off her to go under bridges ... although I quite often used to bend forward and hug her round her neck. The towpath had almost disappeared in places, and in other places the canal was only semi-liquid - full of weeds, silt etc. Just a few short years later canal recovery had become a big thing and the lonely, beautiful dereliction had gone forever.