At ours one lady was trying to hide them as much as possible, then claimed she didn't know the rules. Might have believed her if they had been more obvious......
I used to skate at one rink where normal very light earphones, of the type that were common with MP3 players (this was some time ago) were allowed, but a rink guard complained when I wore full size "studio-type" headphones, that covered the ears, to a public session. Perhaps because full size headphones would block out more of the sound? And perhaps it was the rink guard's own rule.
At most of the rinks where I currently skate, people wear small headphones, including ear plug phones, pretty often, during public sessions. But some area rinks, like Capital Clubhouse, do have rules. I don't skate freestyle and dance sessions any more, but I think that is true those places there too.
In the U.S., in general, rinks can make their own rules, and many rinks allow the rink guards some leeway to make rules for safety. AFAIK, there are no insurance, on earphones and headphones from USFSA or ISI, and even if there were, many rinks use other insurance. And AFAIK, there are no federal or state laws. So it should be expected to vary vary rink-to-rink.
But it is hard for me to imagine serious skaters at freestyle and dance sessions desiring a rule that didn't let them hear their own music, so I am guessing that in areas with many skating rinks for skaters to choose from, most rinks will allow them. However, "program dance" sessions, where pattern dance music is played, and where people skating that dance have right of way, and are sometimes not expected to look out for skaters dancing other patterns, might well be different.
At most rinks I have skated at, it is much more likely that someone would complain if you played something with a speaker, like a boom box, so that other people could easily hear what you were playing!