The usual hypothesis is that a microscopic layer of the surface melts, not because your shoes are warm, but because of the pressure. But the pressure is not enough to do that.
That said, as anyone who has been in icy conditions can attest, it is clear that ice at ~0° C is vastly more slippery than at, say, -20°C.
My understanding is that, at the borders, master is constantly changing between its states. A boiling pot has water molecules turning to steam, as well as vice versa. It just has more of the first probabilistically.
That's more or less it, as far as I understand. There's the hexagonal lattice of solid water ice, where hydrogen bonds form a 3D tetrahedral structure which is very stable. At the boundary, there are no molecules "above" the solid latice, so those water molecules are held less tightly. The exact dynamics are challenging to predict because we can't exactly see what's going on (most simulation based).
The pressure from well distributed static load divided by area is not, but on the tiny scale where the difference between grippy and less grippy surfaces happens there isn't so much "well distributed" going on. And once you add lateral force to the mix all bets are off: there will always be a point getting better grip (is surface interference the correct term?) than others, see a local force concentration and when that causes a tiny spot of phase transition there will very soon be a new point of least local slippyness getting all the attention of lateral force.
", it is clear that ice at ~0° C is vastly more slippery than at, say, -20°C."
There is nothing more slippery in my experience, than rain on the street, that just turned frozen. But ice at -20°C is usually older and has not such a smooth surface anymore, so hard to compare in non lab settings.
If that were the case, then cold things wouldn't slip on ice, but they do (for a demonstration, pick up a rock that's been sitting out in the cold and note that it still slides on ice)
I'm not sure a cold rock sliding across very cold ice will slide any better than if the ice was another very large smooth rock. Ice is hard and smooth. Hard smooth things have low friction.
That would be my reasoning, but it likely seems to be wrong, well why?