Customarily, rather than giving gifts on Christmas, gifts are given on Three Kings Day at the end of the traditional celebration of the Twelve Days of Christmas (which begins with Christmas, rather than ends with it).
In some regions of Mexico, it is traditional for children to leave their shoes out on the evening of January 5, sometimes filling them with hay for the camels, so that the Magi will be generous with their gifts. This is analogous to children leaving cookies out for Santa Claus.