Well the alternative would have been to have remained a handmaiden to Mama dearest, Alexandra, like her sister Victoria. Maud was already in her late twenties, old by princess standards of the day. I think she and Carl had plenty in common and he was a cousin, so she knew a lot about him anyway.
Apparently she was rather bored with life in Denmark, however. Healthwise Maud was unsuited to those long Scandinavian winters. She was rather delicate like all Alexandra's children (most were born prematurely, irritating Queen Victoria who liked to be in at the birth of grandchildren if possible.) Maud was very thin and delicate looking. Her waist was one of the smallest I've ever seen. A grapefruit would have seemed huge next to it.