Since this defect in your stairs is known to the club, you must post some sort of sign warning people that the stairs are slippery when wet and to be careful. Failing to do this constitutes a failure to warn of a known defect/hazard on the premises, and opens up the club to substantial potential liability. All you need is for some member or guest to slip and fall, and you'll find yourselves hearing from a lawyer. Injuries in what we call slip-and-fall cases range from embarassment to bruises to broken bones to death from head injuries or heart attacks (from bone marrow getting into the blood stream).
As for the stairs themselves, there is a paint called Skid-Not--it has some sort of nubby things in it that are supposed to make porch/deck stairs and concrete sidewalks safer. I don't know if it comes in a colorless version, or if it can be used on railroad ties, but you could check and see. Also, 3M makes a product called Safety-Walk Anti-Slip Surfacing Roll. It comes with a self-sticking adhesive backing which is probably worthless for you, but you could nail it on. I know it comes in gray and black; I'm not sure about brown. The one I used was 1 inch wide, medium duty. You might want a wider version, and possibly the heavy duty.
Last, but not least, you didn't say whether the steps were always slippery, or have only become so over time. If it is a more recent development, you may very well have moss or algae growing on the steps that you can't necessarily see because of the dark wood. A mild solution of water and bleach and a nice stiff scrub brush will take care of it temporarily--until it grows back again.