Victoria Pendleton was in her 30's when she learned to ride so she could race so age is certainly not really a reason to not give it a go, finding a horse to ride, if you don't already have one, getting both of you fit enough will be more of a challenge.
If you start working now towards racing next season there is plenty of time to find out whether it will be possible, getting pt work riding out racehorses or pointers would be the best way to get started, many will be more than happy to take you on if you are capable and committed, our local trainer has people riding out on Sat am because it is a busy day for staff so having a few extra riders is useful.
Find your local National Hunt yards and offer to ride out -even if it is just saturday mornings to start with. You will soon discover if you really really want to do it and are brave enough.
Unless the yard has an old schoolmaster that they would let you have a spin on you are probably going to have to buy and train your own horse to start with. And thats where it gets expensive.
Jamie Alexander has been winning ptp's and indeed the Hunter Chase at Kelso the other day - he is 54! So age is but a number!
Eta - I see from another thread that you have previously had a serious spinal injury. Because of this a doctor may not pass you fit for race riding. You would need to pass a medical before getting your licence regardless so please do look into the options and speak to your dr before you do anything or spend a heck of a lot of money chasing a dream that may not happen.
I've worked on yards for the last 10years just never a race yard.
I've worked with big fit hunters for the last 5years and had a few ex racers for exercising and getting fit to go team chasing (I haven't ridden them chasing but did do a novice on my mare).