Can Spider-Man climb ice walls with his hands and/or his web?
Are there examples where Spider-Man encountered ice, or other evidence of his superpower under cold conditions?
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The Marvel Universe Wiki describes the wall-clinging ability as a "ability to mentally control the flux of inter-atomic attraction (electrostatic force) between molecular boundary layers."
Basically, his stickiness is due to a telekinetic ability to increase attraction between surfaces on a molecular level (akin to increasing the static charge on a balloon). Theoretically, he'd be able to do this enough to stick to literally any surface, regardless of how slippery the surface is. I'd imagine it would only take an increased concentration on "being sticky."
I read somewhere once that due to the telekinetic behaviour of his abilities, he isn't allowed to play poker with the Avengers.
As seen in The Amazing Spider-Man Volume 1, issue 92, page 5, last panel... ...Spidey can't stick to ice.
Ice is solid water. It has a low coefficient of friction when a layer of water forms between it and whatever is rubbing on it - think ice skate. Without the layer of water, it is just another solid.
Spider-man's climb is, in theory, about microscopic hairs that work like ice-climbers picks into all surfaces. The kind of friction normal hands have is about bulk-surface against bulk-surface. One of the consequences of the hair-bridge is that it is going to be a poor conductor of heat when contrasted against the bulk friction of a normal hand. Heat transfer is about cross-sectional area and the hair-area is negligible compared to the surface area of the hand.
Bottom line: If he can climb smoothed concrete, then he can climb ice. It is going to work better if it is not right at melting point or soppy-wet though.
Links to answers about how 'Spidey' climbs:
In general they are muscle-control driven biological microstructures. The points above about applicability to concrete/solids, melting points, and heat transfer apply to the biological microstructures as long as they are not a biological analog of a heat-pipe.