Ice and mixed climbing require highly specific set of skills, that are not too easily gained by doing anything else. And yes, this includes rock and gym climbing too. Furthermore, the game is largely within the head. Best way to improve your confidence in ice climbing is to ice climb. Failing that, drytooling and rock climbing and even indoor climbing can all help.
However, when none of these are an option due to accessibility or time constraint, there are quite a few exercises that can be performed at home with not much equipment and that don't take too much time to complete.
Swinging. Take ice tool and duct tape some weight to head (say two cans of beer). Then start doing swings (aim for precise swinging that matches actual ice climbing swings). Depending on your fitness, weight and swinging speed, 40-60 repetitions per hand and a set should make the hand properly pumped. If it doesn't increase the weight. Repeat three to four sets per hand.
Calves. Bog-standard toe raise, either each calf separately or both at once. Or mix and match. Repeat between 40-60 times. If it doesn't start to burn your calves properly, either put your toes on a platform or put a backpack on.
If you have a pull up bar, there are lots of possibilities. For variety and added specifiness you can use the bar, hang from it from your tools or attach rock rings to bar. Of course there are the classics:
- dead hang
- one handed dead hang
- pull up (normal, staggered)
combination exercise consisting of
- pull up - lock off combo (repeat until properly pumped or until you can't do a pull up anymore)
- dead hang for about five seconds
- pull up
- lock off for roughly five seconds either at top position or lowering my arms to 90 degree angle
- to allow me to stay on, I place my feet on a bad support (small climbing hold bolted on wall in my case) to take some off the weight off my hands (not too much) and allow to shake out
- keeping my feet on the support, few repetitions of a pull up, lock off and reaching higher with another hand (as in reaching for the next hold)
- another shake out
- few repetitions of dead hang and shake out placing feet on support
- finish with dead hang until the pain becomes unbearable. Alternatively just hang while keep feet on a bad support (easier, thus allows for more duration).
Another simple exercise I find effective is to do a lock off (in 90 degree angle) while raising my feet (curled up) towards chest and keeping them there. This puts a load both on arms and core. This can very well be be combined with pullups by doing a pull up, keeping the lock off & feet raise for a few seconds, then repeating as many times you can.
Step up. Build a two or three step ladder, put a backpack on and start stepping. Unlike StairmasterStairmaster, this does not cost much, does not make much sound and doesn't take too much space. You don't have to use time to get to the training and you can train no matter of the weather. Obviosuly this is monotonic, but this can be aided by doing it in the living room watching tv or listening to music. Height of the steps and weight of the backpack obviously make a great difference in how strenuous this is. I use this exercise mainly for aerobic endurance, so I usually do this for an hour non-stop, changing the "leading" foot every five minutes. Mimics walking uphill with a backpack far better than, say, running, cross country skiing or mountain biking, although this certainly isn't as much fun. Trains both general aerobic endurance as well as uphill specific muscles of you feet. Add toe-raising on top step to make it harder.