Enables the directed movement of pyridoxine across a membrane into, out of or within a cell, or between cells. Pyridoxine, 2-methyl-3-hydroxy-4,5-bis(hydroxymethyl)pyridine, is one of the vitamin B6 compounds. Pyridoxal, pyridoxamine and pyridoxine are collectively known as vitamin B6, and are efficiently converted to the biologically active form of vitamin B6, pyridoxal phosphate.