But the dwarfs actually sing, "Heigh-ho, heigh-ho, it's HOME FROM WORK we go."
In fact, "off to work we go" is so engrained in us, that you STILL probably think they sing it at some point in the film. Which is true. They do. Just not where you think.
CORRECTION: While the lyrics to "Heigh-Ho" don't include the words "off to work we go," the dwarfs sing it once at a later point in the movie. An earlier version of this post misstated that they never sing it. (3/18/15)