I have several bridges in my world, which uses the Fantasy Texture pack. The bridges along the horse trail between my houses are set up simply, just two sideways parallel oak logs with two rows of oak planks in between, making a span of four blocks crossing the river. The bridges are completely flat, and anywhere from 3 to 8 blocks above the water.
Ever since the update, riding a horse across these bridges causes me to take a minor amount of damage. I have maxed out enchanted armor, so the damage doesn't even register, but I take noticeable and audible hits. The horses aren't affected.
I also had this problem in a friend's realm, taking damage across one of her flat, 3-block diagonal spans across a stream.
However, the two arched bridges I have, which are made of a variety of stones, don't cause this damage. These bridges are wider and arched, with steps leading up the archway on both sided, in addition to being made of various kinds of stones, and are right near each other, whereas the flat wood bridges that do cause damage are located in different areas over different bodies of water.