Riding a horse into the water causes the player to 'fall off' of the horse. Horse is no longer controllable and the client acts like the player jumped off, allowing for normal movement and HUD. Placing blocks is, however, impossible if the player is too far from the horse, similar to the old Ghost Mode with e.g. boats on soulsand. Player is also stuck in sitting position in both F5 and inventory screen. True Ghost Mode remains unverified, since this was all found in SP: other players may or may not be able to see the player in Ghost Mode. It is easily fixed by sneaking, the default for dismounting, but it will not drop the player off at the horse but rather leave the player at the position before sneaking.

Note that this only happens if the horse sinks, i.e. the horse's head is submerged. In a 1-deep body of water the player will remain seated.

Unverified: The bug only persists for as long as the horse remains in a body of water of more than 1 block deep. Bug did not seem to happen when the horse swam to a 1-deep spot.

Final note: Cheats were on, so the F5 shot was taken in creative while messing about with flying in seated position. Couldn't resist. Other 3 in order:
1: before placing the rail
2: after placing the rail
3: after right-clicking once more