Unfortunately Not a Real Pony

I've seen a few stories going around to the tune of "in the Soviet Union we weren't allowed to have pine trees on the holidays" and it always confuses me because my ex-Soviet friends (or rather, their parents) always told me that they were allowed to have trees, except they had to call them New Year's trees and the star on top had to be red and five-pointed (like communism). Also they gave presents... on 1 January.

Basically, Christmas with the serial numbers filed off.