I think most of ice climbing is actually reading the medium rather than using strength, technique or mental toughness. I'm skeptical of home training methods because of this. power is never a bad thing to have in excess, but it's the wrong thing to focus on. the best thing you can do is simply to get mileage in as many different types of conditions as possible--rotten & aerated, cold and brittle, wet and warm, blue and plastic.
once you've learned to read the medium, it's all about mastering the movement. as many people have said, if you're getting exhausted on an ice climb, you've already failed. if this happens to you, getting stronger and tougher will not solve the underlying problems in your approach. there is a right way to move on ice. it's almost like an algorithm. place one tool high, hang like a monkey, get two good foot placements at knee level, stand up straight, hips in, repeat. after you've mastered that, learn to get bomber tool placements with as few swings as possible. if you can master these two skills, 90% of your technique problems are solved.
the rest involve awkward positions that the algorithm won't help you at all for. for example, any time your shoulders are forced into the ice for some reason, forcing you to chicken-wing your next tool placement. I personally have far too much mileage in awkward positions, usually because I'm not trusting my tool placements enough to lean out on them. learn to avoid them in the first place.
it helps to seek out climbs that are awkward for you. hobbit couloir, hassig's direct, and super goofer's all stick out in my mind as climbs where a little better technique would have saved me a lot of energy. anything that's weird will be great for you.
ok, my rambling has far exceeded my credibility on the subject. for better tips than I could ever give, read everything will gadd has written on ice technique on his blog. this post in particular: http://willgadd.com/category/blog/page/7/
have fun out there!