If you happen to play a musical instrument which is easy to transport, bring that too. It would be a good idea to bring a few small typical gifts from your country to give to your host families. But do not buy anything expensive. Pictures, booklets and scenic tourist - pamphlets are good alternatives. Do not forget your camera so that you can preserve your impressions for the years to come.
Film is on sale everywhere in Denmark.
It would be a good idea to keep a diary right from the start. The diary can be detailed or simply short notes to back up your photos. Without notes you will return home and find yourself with a lot of pictures which you cannot separate from one another. Do not bring skiis or skates with you. It is by no means certain that you will have the opportunity to pursue winter sports.