It depends upon what you're asking of the mount. If you're asking for just general ride, an unskilled rider may be able to ride a mount with assistance. Think of a real life situation, if you've never ridden a horse can you ride one even if it's already trained?
For a horse, who would saddle it for you? Or if you prefer to try riding one bareback, you still need to mount the horse. You could do this unskilled Dex/athletics check; but then you still need to get the horse to go where you want it. An untrained rider may get the horse moving, but don't be surprised if the horse may not go where you want to because you're giving it mixed signals (e.g., you're giving signals with the reigns and with pressure from your legs). In general, even just riding a calm, docile mount can be a challenge for an unskilled rider without assistance.
Now, here's some situations I think could never be performed without some level of skill in riding:
- stopping a panicked animal (e.g. runaway horse)
- forcing an animal to jump an obstacle if untrained
- fighting from an animal
Riding an exotic animal would probably be more difficult, unless the animal was able to communicate with the rider and didn't mind being ridden. For an intelligent animal with an unskilled rider; the rider would probably have to rely on strength/dexterity or some other skill checks (e.g., athletics) to hold on in difficult situations (e.g., flying through a storm; aerial combat)