Is there no summer ice where you live? When I was young, I had to change rinks for the summer, but it was do-able. Now it seems more rinks are year-round. Have you asked your coach this question? S/he will certainly have great advice for you.
I think I might look into an adult ballet class, if there are any available? What about yoga? I always loved yoga, and it has the added benefit of meditation, which can help with the mental part of skating (especially, but not limited to competitions!). What about some form of martial arts, like kungfu or karate? I know Elvis Stojko (sp??) practiced martial arts in his olympic days, and it showed (in a good way) in his skating.
I also always find my workouts are more effective when I'm working with a personal trainer. At most gyms you can do this. They'll try to push having the trainer with you all the time, but I used them like a skating coach- one training session a week, then I'd work on my own. You can see what your budget allows for. They could direct you to exercises that would address your personal goals and needs. And perhaps free you from the hated Zumba!
There are also some skating related fitness videos- I've been using Sk8strong and like it. The owner is on these forums,and is very responsive and helpful, so if you have any questions about her products, she's absolutely there for you.
Others will probably have some even more interesting ideas!