Ice climbing requires overhead strength to swing an ice tool as well as core-strength to stabilize while you swing and move upward. It also requires good leg strength and endurance, especially in your calves.
The strength needed for climbing ice and mixed terrain can be broken down into core strength, upper-body strength, and general endurance. There isn’t much aerobic demand in this sport. It is recommended that you work on your strength and endurance by working out in the gym or by rock climbing.