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The more advanced brands of in ear would be fine, and trying out some "dollar store model" isn't going to give the same fit experience etc.>Wireless in-ear, bluetooth capable, waterproof would be good for sweating.
Is that a common problem with headphones? Since I mostly use headphones at home, while sitting, and I don't sweat much at ice rinks, that isn't an issue for me. Maybe "closed back" headphones would be the worst. And behind-the-ear bone conduction models would be the best?
If she chooses earbuds, and they tend to fall out because of her ear shapes, some earbuds have a curved piece that fits behind the ear, and helps a little to hold them in. You can maybe try to check whether ear buds will stay in her ears securely by trying a cheap pair at the dollar store. To stay in well, the ear canals have to be substantially wider next to the eardrums than at the outside, and unusually narrow ear canals don't work with most earbuds regardless.
Even if she won't use them on ice (and maybe she will eventually want to hear her program music while skating), rink air is usually quite humid. A lot of electronics doesn't cope well with that. So water resistance is good. Maybe it would be good for sweat too.
I think of it a compact lightweight headphones or earbuds that includes its own flashdrive to hold recordings without connecting to another device would be better. I haven't tried any of those devices, but it makes sense. Because the separate SmartPhone or similar device can sometimes be awkward to attach to the body, and might fall off or affect balance if she practices rotating jumps with them, even off-ice. BUT I admit there is a "cool factor" to high end iPhones, that is more important to some kids (and adults) than all practical considerations. And they are multi-purpose devices - e.g., they can video skating. But it sometimes scares me when people hold distracted phone conversations while skating.
I trust you know that high volume listening can damage hearing over the long run. Some kids (and oddly enough, some adult high end audio buffs) love doing that. It may or may not help to point out how my elderly people need hearing aids - and still have trouble understanding speech. But peer pressure might be more effective than rational explanations from parents, as you may have learned.
I wonder if it is healthier to stay away from "bass boosting" models, unless she has low frequency hearing loss that requires it? I think that encourages high volume listening, and loud bass makes understanding words more difficult. (For English - maybe there are languages where low frequencies help understanding words?)