Well, my advice would be to ask your employer, or whoever is directly above you if that would be okay. Back when I was in college I had had jobs where I was allowed to use headphones. It really depends on the kind of job usually. If it is the type of job where you just have to press a button every 17 seconds (yes, I had that job once), or cleaing up a construction site, raking leaves, jobs that don't require your ears, etc. then there isn't much of a reason for them not to. If it is the kind of job where you will be working with or even around customers, or in a dangerous area where your ears might be of use for the sake of keeping yourself and others out of danger, or where you need to be able to hear your boss, etc. then it would be pretty reasonable for them not to allow you.

Whatever the case is, I would not recommend doing it discretely or trying to hide it (like under your hood for example), sooner or later somebody will notice, and chances are you will have a fellow employee or two that don't like you and would be happy to get you in trouble... or any other number of cases, and if it is against the rules then you might risk losing the job.