No limits. Before I switched to software development I paid my bills as a Jazz guitar -player and -teacher. Observation: the "too old" only applies indirectly when you're "grown up" schedule is already very full with everyday activities. Even then I watched people with no time to spare but with lots of enthusiasm and determination making progress. Some physical learning gets slower with age, but the speed of learning is not important at all IMO/E.
I line up with others here in recommending private lessons, at least for the beginning. Getting quick feedback in what you are doing is essential, especially for the motoric part.
I picked up viola da gamba with 39 and might have lacked some physical abilities to do the bowing well from the beginning but thanks to my teachers I got smoothly over these problems.
Another thing: start playing with others early. It's like chatting away in a new language. You learn best/have the most fun when you have to make sentences and express yourself.
Get yourself an axe and enjoy!