When seeking out lessons / coaching it is always important to know why you are going, as this will change where you choose to go, how often you go, who you choose as your instructor / coach and what type of lessons you need.
Lessons on school horses are ideal for the following situations:
When you are first learning to ride.
To gain confidence on a quiet, capable horse (if your own horse is green or is scaring you in some way)
If you wish to ride as a hobby only (for pleasure or fitness) and do not wish to own your own horse.
If you are temporarily without a horse or without a way of transporting your horse.
If you are working on improving a specific task or skill where a more skilled school horse may be of assistance
For most situations that don't fall into the above categories lessons on your own horse are preferable. Lessons on your own horse are essential in the following situations:
You wish to compete (eventing, dressage, show-jumping) on your horse in the near future.
You are having problems with your horse.
You are trying to assess the horses suitability to you and/or the sport you wish to compete in.