The Wikipedia article on Sadovnikov says:
Sadovnikov has never received due credit even for his most famous poem, Iz-za ostrova na strezhen ("The Carnival is Over"). Set to a popular folk melody, this piece about ataman Stenka Razin is widely considered to be part of Russian musical folklore.

That paragraph has two footnotes, both to articles in Russian, which I can't read at all. But the use of the phrase "set to" suggests that the Wikipedia contributor believed there was a pre-existing folk song or tune that Sadovnikov worked around.

Aren't most folk tunes for dance music? This one is slow and mournful, so I'm assuming it was a song rather than a tune.