With training through handle animal they can do a fair amount with direction from the character. Even animal companions with just a Int 2 still need to use training and handle animal rolls.
It's when the creature becomes Int 3 (at 4th level an animal companion could get this) that they basically become an independent character, no longer need handle animal rolls and can do things freely.
If you are a fighter and want a buffed up mount, one way of doing it is at 5th level dip into Druid for one level and use your character feet to take Boon Companion from the Seeker of Secrets book. With that dip and feat you'd have a 5th level animal companion, which you could immediately give an Int 3 to, along with a bunch of other benefits.
