Will Mounts be able to jump?

[Matsume]

I hope none of the mounts can jump. Chocobos however, they can easily tie this into Chocobo breeding -- For example Red Chocobos could be able to jump, while our favorite Light Blue and Dark Blue chocobos can traverse watery obstacles, while our trusty purp-black/gold (FFIX) chocobos can fly.

Two words: Yoshis's Story (no pun intended)

Furthermore, I am pretty sure Yoshidasan has discussed jumping in one of the LIVE producer letters in which he explains that jumping on mounts is highly unlikely to be implemented. If I knew just where to look I would post the Link, but alas the videos tend to be lengthy (one or two hours) and I am not interested in spending that much time searching for this.