Finally, here's the actual bracket, with transcription (and links to the respective polls) under the cut. Seeds aren't necessarily representative of how I would personally rank each song, but how I think other people might rank them. I like some songs that I think most people would find annoying, so I gave them lower seeds.
Seed in parentheses; winner in bold. The numbers don't quite match because I had to remake the bracket in order to post a picture of it.
Third Round
Christmas Shoes (1) vs. Mistletoe and Holly (18*)
All I Want For Christmas Is My Two Front Teeth (9) vs. Santa Tell Me (25)
12 Days of Christmas (2) vs. Here Comes Santa Claus (15)
Happy Holiday/The Holiday Season (23) vs. I Want a Hippopotamus for Christmas (7)
I Saw Mommy Kissing Santa Claus (30) vs. Santa Baby (14)
Little Saint Nick (22) vs. Baby, It's Cold Outside (6)
12 Pains of Christmas (4) vs. Dominick the Donkey (13)
Grandma Got Run Over by a Reindeer (21) vs. Do They Know It's Christmas? (5)
Second Round
Group 2A
Christmas Shoes (1) vs. Jingle Bells (6*)
There's No Place Like Home For The Holidays (48) vs. I Saw Three Ships (16) Draw
All I Want For Christmas Is My Two Front Teeth (9) vs. Up on the Housetop (24)
Santa Tell Me (25) vs. Wonderful Christmastime (8)
Tie-Breaking Mini-Bracket (Closes 2 Jan)
There's No Place Like Home For The Holidays (48) vs. Mistletoe and Holly (18*)
I Saw Three Ships (16) vs. God Rest Ye Merry Gentlemen (58*)
Mistletoe and Holly (18*) vs. I Saw Three Ships (16)
Group 2B
12 Days of Christmas (2) vs. Jingle Bell Rock (31)
We Wish You a Merry Christmas (18) vs. Here Comes Santa Claus (15)
Hark! The Herald Angels Sing (55) vs. Happy Holiday/The Holiday Season (23)
Deck the Halls (26) vs. I Want a Hippopotamus for Christmas (7)
Group 2C
Happy Xmas (War is Over) (3) vs. I Saw Mommy Kissing Santa Claus (30)
Mary Did You Know? (19) vs. Santa Baby (14)
What Child is This? (54) vs. Little St. Nick (22)
Holly Jolly Christmas (38) vs. Baby It's Cold Outside (6)
Group 2D
12 Pains of Christmas (4) vs. Away in a Manger (36)
Mele Kelikimaka (45) vs. Dominick the Donkey (13)
What Christmas Means to Me (53) vs. Grandma Got Run Over by a Reindeer (21)
I'll Be Home for Christmas (37) vs. Do They Know It's Christmas? (5)
First Round
Group 1A (Closes 16 Dec)
Christmas Shoes (1) vs. You're a Mean One, Mr. Grinch (64)
Rudolph the Red-Nosed Reindeer (32) vs. Christmastime is Here (33) — Draw
The First Noel (17) vs. There's No Place Like Home for the Holidays (48)
I Saw Three Ships (16) vs. Winter Wonderland (49)
All I Want for Christmas is My Two Front Teeth (9) vs. Snowman (56)
Up on the Housetop (24) vs. Silent Night (41)
Santa Tell Me (25) vs. O Little Town of Bethlehem (40)
Wonderful Christmastime (8) vs. Run Rudolph Run (57)
Tie-Breaking Mini-Bracket (Closes 22 Dec)
Rudolph the Red-Nosed Reindeer (32) vs. Jingle Bells (6*)
Christmastime is Here (33) vs. This Christmas (15*)
Jingle Bells (6*) vs. This Christmas (15*)
Group 1B (Closes 17 Dec)
12 Days of Christmas (2) vs. O Tannenbaum (63)
Jingle Bell Rock (31) vs. Let It Snow! Let It Snow! Let It Snow! (34)
We Wish You A Merry Christmas (18) vs. O Holy Night (47)
Here Comes Santa Claus (15) vs. The Christmas Song (Chestnuts Roasting on an Open Fire) (50)
Feliz Navidad (10) vs. Hark! The Herald Angels Sing (55)
Happy Holidays/Holiday Season (23) vs. Silver Bells (42)
Deck the Halls (26) vs. Have Yourself a Merry Little Christmas (39)
I Want a Hippopotamus for Christmas (7) vs. Last Christmas (58)
Group 1C (Closes 18 Dec)
Happy Xmas (War is Over) (3) vs. White Christmas (62)
I Saw Mommy Kissing Santa Claus (30) vs. Rockin' Around the Christmas Tree (35)
Mary Did You Know (19) vs. All I Want for Christmas is You (46)
Santa Baby (14) vs. O Come All Ye Faithful (51)
Do You Hear What I Hear? (11) vs. What Child Is This? (54)
Little St. Nick (22) vs. Sleigh Ride (43)
Santa Claus is Comin' to Town (27) vs. Holly Jolly Christmas (38)
Baby It's Cold Outside (6) vs. Carol of the Bells (59)
Group 1D (Closes 19 Dec)
12 Pains of Christmas (4) vs. It's The Most Wonderful Time of the Year (61)
Little Drummer Boy (29) vs. Away in a Manger (36)
Frosty the Snowman (20) vs. Mele Kelikimaka (45)
Dominick the Donkey (13) vs. Joy to the World (52)
December (12) vs. What Christmas Means to Me (53)
Grandma Got Run Over by a Reindeer (21) vs. It's Beginning to Look A Lot Like Christmas (44)
Blue Christmas (28) vs. I'll Be Home for Christmas (37)
Do They Know It's Christmas? (5) vs. We Three Kings (60)