There is no perfect rhyme for reindeer that is one word and has to do with Christmas. With two words you could do Christmas cheer.
Australians use kangaroos instead of reindeer at Christmas.
rudoff the red nose reindeer
There were 8 reindeer in the poem twas the night before Christmas.
if your referring to reindeer's that pull a sleigh, its the Christmas spirit or its either 'magic' reindeer dust.
Rudolph the Red-nosed reindeer is the obvious answer
Reindeer are a popular decoration for Christmas so there are many stores that carry reindeer during the Christmas season. Try stores such as Target and Michael's. Online sources are numerous. You can check out Reindeer Decoarations website that offers a huge assortment of reindeer decorations.
reindeer
Christmas eve
Santa Claus's Reindeer pull the sleigh on Christmas Eve night.
He is the guide reindeer on Santa's sleigh on Christmas eve.
Doves, Christmas trees, reindeer, stars, and santa Claus