The versions I've heard have a long chorus with two sections, as in Masato's post. Here's a transliteration of the Russian (per spelling, not phonetics):

Tarybary, rastabary,
Snezhki bely vypadali,
Sery zajtsy vybegali,
Oxotnichi vyezzhali,
Vse sobak svoix spuskali,
Krasnu devku ispugali.

Ty, devitsa, stoj! Stoj, stoj, stoj!
Krasavitsa s nami pesnju poj, poj, poj!
Chuvil', moj chuvil',
Chuvi[ra]l', vil', vil', vil'!
Eshchjo chudo, pervo chudo, chudo rodina moja!
Eshchjo chudo, pervo chudo, chudo rodina moja!


Talk and gossips,
White snowflakes fell,
Grey rabbits ran out,
Hunters rode out,
Let all their dogs loose,
Frightened a beautiful girl.

You, girl, stop, stop, stop, stop!
Beauty, sing a song with us, sing, sing, sing!
Bird, my bird, birdie-dee-dee-dee!
What a wonder, the foremost wonder, the wonder of my homeland! [2x]

Each section begins slowly and accelerates into a tongue twister.

Also, the title and first line usually contain the diminutive "berjozon'ka" (phon. beer-YO-zuhng-ka) instead of "berjoza"; this is metrically consistent with the other verses.

Do svidane!