Water evaporates at all temperatures significantly above absolute zero (which we cannot reach anyway, and don't call me a liar if a quantum physicist points out that a quantum fluctuation might eject the occasional water molecule, absolute zero or not!)
Ice, you ask? Surely water doesn't evaporate from ice? But it does. Ice will dry-evaporate quite actively into a brisk breeze in very dry air. They call such dry evaporation sublimation. In freezers it causes what they call freezer burn. And if conditions are not very breezy, the vapour is likely to re-freeze into fine hoar frost.
Such sublimation (a sort of freezer burn, if you like) is used in microscopy to etch broken ice surfaces of frozen specimens to show ultramicroscopic cell structures without chemically fixing or staining them. And the resoution of the best shots is STUNNING!
Water evaporates at all humidities as well.
To understand the implications of the question and its answers so far, remember that what we usually mean by evaporation is NET evaporation, the visible decrease in water, the "drying out". (And remember of course, the other side of the coin, where the visible water increases by condensation.) All those things are real of course, but they are only part of a continous two-way traffic.
The water molecules everywhere are bouncing about all the time, bumping into each other and everything else in the neighbourhood. If one bumps into a liquid or cold surface, it is likely to stick there. We say it has condensed. If it gets bumped hard enough to leave the surface, it is likely to fly off, or be crowded off and carried away in a breeze. We say it has evaporated.
The colder it is, the more slowly the molecule is moving on average, and the less likely a molecule is to bounce out and evaporate, but there always is evaporation, so iron in a moist place is likely to rust and sugar or certain salts are likely to go moist, even in the cold.
Did you know that Antarctica is the most desert of all the continents? In the sense that it has the smallest amount of water falling, even as snow? Whole areas of Antarctica are so dry and windy that the ice is subliming faster than the snow falls, and the ice cover is shrinking. This has proved very exciting for meteorite hunters, because meteorites that had landed in the snow perhaps hundreds of thousands of years ago, are being exposed by the sublimation, and this makes such fields the world's best meteor-hunting grounds!
But wherever you may be, water is evaporating all the time, and condensing as well. What controls the visible behaviour is the BALANCE between evaporation and concensation. If more condenses than evaporates, the amount of liquid or solid water increases, if less condenses, it decreases ("dries out") And the faster the evaporation or condensation, the faster the drying or increase in water or ice or hoar frost. And the faster the breeze carries the vapour away or brings it in, the more dramatic the results, transporting water and heat in one direction or another. By playing with misting on glass or mirrors you can learn a lot about such things.
Have fun!
Jon
