A very long paper here on friction of shoes and hands and how it impacts climbers. This is good news for the upcoming winter season:
“Similarly climbing shoe manufacturers design their shoe rubber to work best in a specific temperature range (0-5° centigrade), below this the rubber is harder and won't mould well to the shape of the rock and above this the rubber will be too soft and will deform too easily. This why climbing shoes work best in the cold.”
“The cold has a two pronged effect on our hands. Firstly our hands sweat less and secondly our skin becomes harder (the cold reduces the fluidity of the liquids that constitute our cellular membranes). Dry hard hands have better friction than soft, damp ones.”
Lots of formulas for our engineering friends too.