In reply to ojp:
Sounds like cold dry skin. I'd try a bit of moisturiser and warm you hands up well to get the skin supple before climbing.
How much moisturiser your hands can take can be a bit tricky, too much and my tips and the fleshy bits start to tear (light surface wear but it really uses up precious skin depth) especially when they're soft in the summer.
No idea how good the climbing branded stuff is, I just use E45 or Neutrogena hand cream.
jk