It *is* the exam period, or they *are taking* exams

"These days, undergraduates are taking their university exams. So everyone is studying hard." Or "It is now the examination period at our university, so everyone is studying hard." Or, informally, "It's exam time. We're all studying hard!"

You could say: "Students are in the examination period."

At the moment, university undergraduates are undertaking their exams so everyone is studying hard