I am going to Copenhagen in March. I want to know if I can book the flight now at the airport in cash.
One or two months before you're traveling is certainly not too early to buy a ticket.
Whether you can buy it with cash depends more on the airline you will be traveling with than where you're going. Many low-cost carriers sell their tickets exclusively through the web, but with a traditional airline it should be possible to buy a ticket with cash still.
This doesn't mean you should necessarily go to the airport to buy it. Most airlines have cut down significantly on how many manned ticket counters at airports they have, compared to decades ago. If you know the airline of your choice has a ticket counter at the airport you want to travel from, you can go there, of course -- but in general it's just as convenient to go to a walk-in travel agency closer to you and have them issue the ticket for you.
I wouldn't expect the airline's own ticket counter to have any fare offers better than what travel agencies also get. On the other hand, online-only promotions will be available at neither place.