The only singificant Swedish influence on what Santa Claus looks like is that the Swedish-born artists Haddon Sundblom whose Coca-Cola advertisements in the early 20th century did much to shape the popular image of what Santa Claus 'should' look like. The American 1823 poem "A visit from St Nicholas was perhaps the single largest influence in that area though.

A Santa Claus equivalent did not come about in Scandinavian culture until the late 19th and early 20th century. It's mainly a British-American influence. Prior to that, presents were delivered by the Yule goat, which was a tradition that'd existed for at least a few centuries before that, and might have originated in Medieval venerations of Saint Nicholas, making an indirect connection with Santa Claus.

In Swedish and Norwegian the 'Santa Claus' figure is known as the Christmas gnome (Jultomten/Julenissen), basing him (in name at least) off another folkelore character, one that was really quite different. In Finland, the human figure is still simply called the 'yule goat'. (Joulupukki/Julbocken)

Some source: Schön, Ebbe: Julen förr i tiden (1980), Vår svenska tomte (1996)