Vintage snowboarding footage from 1977 Feb 13 2014
From 1977, a video of someone snowboarding on one of the first commercially made boards:
I'm not completely sure who the rider is (probably Dimitrije Milovich), but the board is a Winterstick. A company who owns the Winterstick trademark still makes a version of the split-tail board you see in the video.
From what I can tell, Winterstick was the first modern snowboard company but was quickly eclipsed by rivals Sims and Burton, with Burton emerging in the 1990s as the growing sport's 800 lb gorilla.