Ice climbing is similar to mountain climbing.. However, instead of being on hard stone, ice climbers move up, down, and even across walls of cold, glassy ice. There are two types of ice climbing. The first type involves climbing over ice and hard snow on the side of a mountain or glacier. The second type involves climbing up water that has become ice - for example a frozen waterfall. Climbers say that both can be difficult and that both require very 5erious attention.