In reply to Bruce Hooker:
>...cold air holds less water vapour than hot air...
This is nonsense though. Air is a mixture of gases; cold air can have just as much water vapour within it than hot air and vice-versa. It doesn't make any difference to think of air as being 'saturated' with water vapour, any more than you could saturate air with nitrogen, for example.
What is true is that when the air cools a larger amount of whatever water is there will condense into raindrops or fog or dew. However, it's a mistake to believe that colder air always means more rain or fog or dew; the amount of water in the air is just as important and that depends on more complex weather like where the air came from and how much ocean water it absorbed etc etc.
So you can have cold, dry days or cold wet days and you can have warm dry days and warm wet days. Which is more likely depends on the details of your prevailing weather systems, but not on the air temp as much....
...which all has very little to do with the topic of friction on rock. So here is a brief summary of my opinion (which is of course definitive).
It is a mistake to think of climbing friction in the way you're encouraged to at school (i.e two flat surfaces moving across each other). We could call this type of friction 'sliding friction', and it has little to do with what happens when climbing. Most of the time we are stood on small edges, and are pulling on small edges. In this case what matters is how easily the skin or rubber deforms under load. Rubber or skin which deforms or tears under load easily will creep off edges and we'll experience bad friction. Equally importantly, rock is not smooth. There are plenty of crystals and pits in the surfaces of most rock and, for the best friction, we would like our rubber or skin to deform a little bit so it can match the shape of the rock, giving much improved holding power.
So there's clearly a balanced to be reached - when hot our skin and boot rubber deform too easily, and roll off edges. When too cold our skin and boot rubber is too firm to meld into the surface of the rock and we'll experience poor friction. People often call these conditions "glassy".
Obviously this is quite a complex balance which will vary between different shoes, skin types, body weights and rock types. So there's no clear answer to whether friction is better if it's cold or not.
Then there's the complicating factor of moisture and sweat. Pure water tends to stick to surfaces (you can see it running down panes of glass which are beyond vertical, for example). This property can allow a thin film of water to act as a "glue" between surfaces, increasing friction.
This is "sticky damp" - a condition beloved of limestone devotees in the UK. Too much water means your boot or skin will mainly be in contact with water, not rock. The friction in this case will be horrible. You might expect sweat to behave similarly, but sweat is not water. It contains oils and fatty acids, which act as lubricants. Consequently, sweat reduces friction dramatically. Therefore, the best friction will occur when it is cool enough not to sweat. Again, this varies from individual to individual.