EDIT: OP, I see we posted at the same time!
I think with your goals, it wouldnt hurt to play with running barrels- just be easy on your horse.
I would consider what are your goals for her?
If you are wanting to seriously compete in higher level competitions, 15 is likely too old, for the reasons above posters listed.
But, if you are wanting to fool around at playdays or gymkahnas, and care more about having fun than winning, I wouldn't think the horse is too old.
However, I know it is very easy to sour a horse on barrels by over training, practicing too much, etc., and unless your horse really enjoys it, at her age that is probably even more likely.
If she enjoys it, though, and you take it easy and worry more about precision than speed, it might be a fun thing to try.