Traditionally speaking, composers throughout history have either been keyboardists of some sort or violinists. The reason for this is that before the advent of technology, the piano was the primary source for playback for a composer - thus, if a composer wanted to hear what they wrote, they had to learn to play the piano. As far as violin goes, I can only estimate that it is because its lineage (along with the rest of the string family) predates the large majority of other instruments.
That said, technology has in some ways replaced much of the old tradition. Now, a composer doesn't have to be a competent pianist in order to write - the computer plays everything back - albeit a bit unrealistically.
Learning to play an instrument is beneficial for composing for a few reasons:
1.) You can play what you write for others! You can share your passion and joy with those around you, and that is something that is very enjoyable in itself.
2.) It helps make your music more expressive. It has been said that the music you write can only be as expressive as you yourself can be expressive on an instrument. Learning an instrument for composition has more to do with learning how to express things musically than rigid technical mastery.
3.) It provides invaluable insight into the way instruments handle - how to write idiomatically for each instrument. This is important for helping performers to sound their best while also making the music rewarding for both you and them as well.
4.) You don't have to master the instrument. Even just a basic understanding about how an instrument works - that is, how it produces sound, things it does / doesn't do well - can significantly improves a composer's writing quality.
5.) Talk to people who play instruments. I love doing this and it is very helpful. They've put in all the time and effort learning the instrument, and they can share their knowledge with you. Going along with this, also have people play sections of things that you're working on. This can give you a clear idea of the sounds you're looking for.
6.) Lastly, don't feel as though you have to pick a particular instrument. Regardless of what you do, all that really matters is that you try to find an instrument that you enjoy playing - for the sole purpose of playing for simple enjoyment.
That all said, it is important to be realistic about your goals. I'm definitely not suggesting that you should stop everything your doing, rush out, and purchase a really expensive instrument. That's just silly.
You don't have to know how to play an instrument to write music - thousands of people do it every day. I merely suggested it as a means to help you increase your writing ability.
Finally, I don't believe someone is ever "too" old to learn new things. I just read an article today about an 87yr-old woman who earned a college degree. Things like this are always inspiring and motivating.
I hope that helps.