Tire Tread and Technique both play an equal part in maintaining tracking on hills (up and down).

When climbing, try scooting forward on your saddle (might be a tad uncomfortable, but it won't last long) and lowering your chin close to the handlebar. No, really, closer than that! WAY down. Sounds wierd, i know, but seriously, try it. You'll be surprised how much more traction you have in this position when climbing.

Decending tracking is all about weight balance and brake modulation. Takes practice, and lots of it, along with the ability to trust your balance will prevail when traction doesn't.