I'm always reluctant to classify things like this as "mint errors", a the coin appears to have been struck normally, even circulated for a while, before the damage somehow manifested itself. As hinted at by other responses above, snapping a coin clean in half is really hard to do, but not impossible. It certainly does not need to be explained by the coin having some kind of mint-created defect.
I don't think "liquid nitrogen" is an adequate explanation for this specific coin, though; a 1962 5 cents is made of pure nickel, and unlike regular steel, pure nickel does not become brittle at liquid nitrogen temperatures. Pure nickel does, however, become more brittle when heated to over 500 deg C.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis