Your situation is pretty similar to mine- I was as horse crazy as it gets as a kid, but didn't get to start riding until I could both pay for it and drive myself. I've been riding for about 8 years now and the more time I spend with horses, the more time I want to spend with horses, to the point where I wish I could switch careers to something horse-related.
That desire to have kids eludes me, too. Fortunately for me, DH is of the same mindset (although it's unfortunate for his mother, since he's an only child)
Honestly, I don't know how I would manage to balance my job, my horse, and a kid. I certainly couldn't keep my current position (which requires me to fly to California twice a week on top of being a fairly high stress position to begin with)
As Cat said, though, it's not necessarily an either-or type situation. Half leasing can be a great option when you're looking at starting a family, both from a financial perspective and from a time perspective.
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon