Huh - I took some group lessons from certain Russian & Ukranian skating coaches. They had the kids run up and down very steep stairs, as well as bleachers, which I thought a bit dangerous. But if you (Diane) did that too (though I don't know how steep they were), maybe it is standard.
They also used a trampoline. A bit iffy for the adults - the particular trampoline wasn't stiff enough, and we touched the floor through the trampoline. But some of the kids did amazing things. Of course, trampolines can be a bit dangerous too - especially if they don't have an outside fence that prevents you from falling off or hitting a body part on the rigid edges - but a lot of people use them. It's kind of fun.
They also (in preparation for Dance or Pairs) had the boys lift the girls. The girls ran up to the boy, and the boys continued the motion into a lift. Again, potentially pretty dangerous for both partners, but a lot of sports are. You can also get lift experience in some types of somewhat advanced performance dance classes. Maybe you could talk to a dance teacher (e.g., ballet, modern, contemporary, ballroom, etc.) to determine whether they could help. But maybe you only want to do singles skating, and this is mostly irrelevant - though many skaters start in single, and change to Dance or Pairs. BTW, there are many different types of lift - even in skating. In some styles the lifted person is overhead of the lifter (as seems most common in pairs), in some the lifted person has to have some body part below some specified part of the lifter's body, like the waist. It sounds like the first should be harder, but the second style actually might place a greater strain on both partner's spines, which is often countered with specified muscle tensions to prevent injury.
And they did a lot of stretching, strength and endurance training exercises - similar to what you might encounter in Yoga or performance dance classes. Other skating teachers have had me (and others) do that sort of thing too.
I personally like to switch off between paddling (kayaks) and skating. And of course jogging, running, hiking, backpacking, and skiing, all preferably including hills, and swimming. Not altogether the same muscle groups as figure skating (though done "right", paddling involves a lot of spinal muscles), and not the same body positions, but I'm more interested in staying more fit and enjoying the outdoors than I am in competitive skating, which would be a lost cause for me. They also are much more social activities than figure skating usually is - though roller and inline skating can be social too.
Some figure skaters also do hockey - maybe including street hockey, which can go in the summer too. Definitely dangerous, even with the appropriate safety gear. (Though some rinks and coaches have told me more figure skaters get seriously injured than hockey players...) They don't really go for grace, but balance and muscle strengthening look similar. Also, quite a few figure skating coaches also teach hockey players, because some hockey players and their families are willing to pay for "Edge" classes and private lessons (sometimes at higher rates than they can earn as figure skating coaches), and because it expands the number of sessions they can teach at. So if you envision a future in which you try to make a living as a coach, I wonder if a little hockey experience would help... Personally I'm afraid to try.