This is a 1960s Soviet-made postcard. It features two anthropomorphic bears, an anthropomorphic rabbit, some birds and an evergreen branch.
The Russian phrase С Новым годом! means "Happy New Year!" (I haven't yet been able to translate the word written in cursive on the red ornament. Feel free to lend a hand if you can.)
According to this article about Russian New Year postcards on Postcardy.com:
"During the Soviet years, Christmas celebrations were not allowed in Russia and the Soviet Union. New Year's celebrations that were similar to Christmas celebrations elsewhere began in the 1930s. Ded Moroz (Grandfather Frost) took the place of Santa Claus at children's parties. He was given a grandaughter, called Snegurochka (Snow Girl or Snow Maiden), to help him. At first the New Year holiday was for children, but later it became a holiday for everyone. ... A real revival of Russian greeting postcards occurred in the 1960s. Although the artwork became more modern and international in style, the themes often show typical aspects of the Soviet and Russian culture. Many of the designs also show a decorative folk art influence."
Postcardy.com also tells us that С Новым годом is pronounced SNO-vim GO-dahm. The article there contains a number of beautiful vintage С Новым годом postcards, so you should go check it out. (It also explains how most of the animals that appear on Russian New Year postcards have their origins in fairy tales.)