This is one of my all time favourite movies and if you e-mail me I could send you a video. There is at least one drinking song it goeth thus:

"If we drink we will die, If we don't drink we will die. So we might as well say what the hell, and let our glasses clink."

There is another song that goes something like this

"We are the cosacks! We are the cosacks! Souls no man on earth can tame..."

This is actually quite a long song, I'll have a squint at the video tonight and post the lyrics tomorrow.