As far as I know, Frederik IX appointed a regent before going on a long trip to Greenland in 1952, but I don't think it's done nowadays when the monarch visits Greenland or the Faroe Islands.

The Royal House has in fact established the practice that no regent is appointed if the King is on a visit abroad that does not require an overnight stay. This has previously applied to short visits by car to Sweden and Germany, but last year no regent was appointed either when the King flew to Poland on a brief visit.