Rock climbing and carpentry might vie as the second-best training. Rock climbing teaches you movement, confidence, and safety in the vertical world. The body positions and fluid movement of the rock climber are powerful tools on ice. Carpentry teaches a wicked swing, and makes a person fit.
Every climber can benefit from increased aerobic fitness.
Ice climbs often involve long approaches at high elevations. The fitter you are, the faster and less oppressive the approaches will be, and the more rested you'll be on the climb. Skiing, running, hiking, and cycling, especially on hills, will help your ice climbing. Never overlook the benefits of strength training. Weight and gym training can pay big dividends, allowing you to climb harder, and avoid or rehabilitate injuries.