Since New Year's was the bigger holiday in the Soviet Union by far, most of the Russian songs are in fact about New Year's, whereas the covers of English songs are more about Christmas proper.

0:00 Jingle Bells
2:50 Silent Night
5:25 O Christmas Tree
8:25 White Christmas
14:00 The Little Drummer Boy
17:50 Little Santa Claus
22:39 The Twelve Days of Christmas
28:20 Joy to the World
30:30 Deck The Halls
32:25 Santa Claus is Coming to Town
33:40 Rudolph the Red-Nosed Reindeer
36:00 Let it Snow
37:35 Hooray For Christmas
39:10 We Wish You a Merry Christmas
40:10 Я отошел (I Walked Away)
43:25 Каляда (Kaliada)
45:00 დალაე (Dalae)
47:25 Пять Минут (Five Minutes)
50:10 Заздравная (Grace)
52:50 Новый Год к нам идёт (New Year's Comes to Us)
54:58 Новый Год (New Year's)
58:07 Веселый Новый Год (Happy New Year's)