I agree with J Brun on this. It seems to me that a drainage pipe along the trail will simply help drain the water down the hill and away. I assume that what you want is to reduce the run off as much as possible. You will need to be careful not to destabilise your slope - landslips can be a real possibility if water is mismanaged.
this site has some simple explanations of swales and other water retaining
earthworks for different situations. My gut feeling is that the "fishscale swales" may be most appropriate for water retention for you. As regards the track, you may want to make some features to reduce the possibility of water erosion if your rain tends to be heavy when it comes.
This Californian site which may be of interest, suggests placing large boulders on the inside of the track to slow down water so erosion is less likely - sort of the opposite of what you're thinking of, and using
native planting on contour to stabilise the slope and increase water retention. I hope this helps.