A lot of women find themselves finally getting into horses once they're in their 40s and 50s. The kids are grown, mortgage is paid, career is stable. They finally have the time and money to do something major like that for themselves.
So NO you're not too old. I am 36 and I've been riding for 26 years now, but I live in a blended family, with 3 kids of my own and a stepson too. I also have 3 more stepchildren that have grown out of the house. Think about that. 7 kids.
It will take a couple months maybe even years of lessons before you're ready to seriously compete. But most shows have beginner classes, not just based on age but on ability.
So you'll be showing against other adults as a beginner.
The best thing to do are take some lessons for a while and then lease or half lease a horse. Once you are a competent rider, you can get full or partial use of a horse, so you can ride as much as you like without the big initial investment or ultimate financial responsibility of selling him if things get tight or if Little Angel needs braces down the road.
Then once you've leased for a while you can decide if you just want to keep leasing, or make the big big commitment.
Go get some lessons. But any instructor will tell you: YOU"RE NOT TOO OLD. Now is a great time. DO SOMETHING FOR YOUSELF WOMAN!!