I bought my first horse once I was able to ride all the schooling horses my horse riding club had.
When you feel like you need more, like the level of the horses you are training with is not enought, it will be time to look for your own horse (renting or buying).
I’ve been riding for 6 1/2 years now and Ibe just started leasing my own horse but I plan to buy him soon. It all depends on a lot of different stuff such as your knowledge on horses, your level of riding, financial...
I rode for 4 years when I started to ride other people's ponies. When I could fully care for them and could tell when they were not feeling well, lame or something like that, my mum bought me a horse which I had to work for to pay along. Now I have been riding for almost 19 years and I train horses professionally for an international dealing stable and clients who have no time to ride daily/ work abroad a lot but still want to go on shows. No opportunity to show big classes or internationally due to money issues, but it makes me very happy to see one of 'my' horses place in a big show 😄
I've been riding for 12 years now and I got my first horse last year after loaning for a few months to understand what it would be like. Owning a horse is a huge lifestyle choice and a massive responsibility to take on, therefore I would advise that you loan a horse before buying, as I did. It helps greatly with experience and gives you an idea of what is involved. I'd wait a few more years at least before buying if I were you. The more you know, the better!