Mistletoe has apparently been used as a decoration in houses for thousands of years and is also associated with many pagan rituals.
According to the book "Extraordinary Origins of Everyday Things," by Charles Panati: The church forbade the use of mistletoe in any form, mindful of its idolatrous associations. As a substitute, it suggested holly. The sharply pointed leaves were to symbolize the thorns in Christ's crown and the red berries drops of his blood. Holly became a nativity tradition. The Christian ban on mistletoe was in effect throughout the Middle Ages. Surprisingly, as late as the 20th century, there were churches in England that forbade the wearing of mistletoe sprigs and corsages during services.
Ivy (as in the song above) is a very poor second regarding Christmas celebrations.
Like the evergreens, ivy is also seen as a symbol of eternal life and is used in Christmas decorations but not to the extent of pine, fir, mistletoe and holly.