We require that all of the head is covered, and that any loose hair (like a ponytail) be contained. If you have long hair, you can put in a bun, but your cap itself doesn't have to contain all of your hair.
Students receive jackets and skull caps as part of the program, and you can certainly wear the cap that comes with your tuition. However, if you'd prefer to wear a cap of your own, as long as it it covers your head and any lose hair you have otherwise contained, that's fine.
Head scarves at the current time are not allowed.
I hope this answers your question.