Hypersmurf
Moderatarrrrh...
WRONG. Go back and read what it says. "If the character uses THE skill with a different mount" the characters RANK is reduced. It says nothing about taking the skill multiple times for different mounts. If a character sticks with the new, unfamiliar mount long enough the DM should stop imposing the reduction after a time, as the character will be familiar with it.
I disagree. It says nothing about gaining familiarity with new types.
You choose the type of mount you are familiar with when you take the first rank. Ride [Horse, Pony, Donkey].
That means at 5th level you have a Max Rank of 8 in Ride [Horse, Pony, Donkey], which gives you an effective rank of 3 to ride a griffon.
If you want to ride a Griffon better than that, I don't see anything to prohibit taking 9 ranks in Ride [Griffon] next time you level... and indeed, there's certainly no way listed to "improve" or "convert" your ranks of Ride [Horse, Pony, Donkey] into Ride [Griffon] ranks.
If someone with four ranks of Perform [Play Flute, Play Harp, Play Drum, Play Xylophone] told me that every day, they were practising dancing... that doesn't mean they pick up a free dancing "Perform slot". They need to spend a skill point on it next time they level.
In the same way, just because someone practises riding a Griffon, until they spend the skill points on it, it doesn't change the fact that their ranks in Ride Horse are only partially applicable.
-Hyp.