The giant owl should be the last of the flying mounts fit for characters.
Pegasi are noble winged horses with a couple of alignment-detecting spell-like abilities. Pegasi are sentient, but cannot speak.
The skums are aquatic slaves created by the aboleths. While underwater, they prefer using their natural weapons, but when raiding the coasts on behalf of their psionic masters they use two-handed weapons, such as spears. Skums can withstand tremendous pressure of oceanic depths, where their masters live.
The homunculus is a small construct created from clay, ash, and a pint of the creator's blood. These humanoid automata are weak, but poisonous. Usually used as servants.
Hippogriffs are something between a griffon and a pegasus. Teritorial, savage, but useful as mounts if tamed.
Hell hounds are fire-breathing canines from the Nine Hells of Baator. Presented are the normal hell hound and it's stronger and bigger variation.
Harpies are flying menaces that can lure you somewhere dangerous with their songs and/or pester you with arrows from afar.
Halflings are weak physically, but are quick and stealthy. Still, not much of a challenge.
Dragons in D&D seem unnaturally fertile, producing offspring with all kinds of other creatures. This lens only lists ancestries of true dragons from Monster Manual, but other options are possible.
The green hag is a weaker than the annis physically, but has a broader range of magical abilities.
Leonals are powerful good outsiders that look like anthropomorphic lions. And they can throw fire and place walls of force innately for some reason.