If you have your own horse to learn on IMO that's the best way to go. Get a really good coach, and they will be able to help you with the issues you are having with your horse if you have any.
I have a great coach and he is teaching me on my horse. I have good general riding knowledge and a very good seat but my coach is picking up on things that I would never have seen prior (nor any 'run of the mill' horseperson) and correcting those faults, and my horse is going better than ever before, because I am RIDING better than ever before.
Nothing wrong with learning on your own horse, whether you are a total beginner or an experienced rider, AS LONG AS you have a good coach.