The first part of "Hava Nagila" is in the freygish mode, which has a sharpened third. In most people's music theory it's the third that determines whether a tune is major or minor. The freygish flat second doesn't count either way.

Probably the commonest seven-note mode worldwide throughout history has been the dorian, which is a minor mode by the same reasoning. It's been used for every kind of music imaginable. You can't claim that people only sang sad songs until the major scale came along in the Middle Ages.

I'm not sure where this "minor=sad" cliche came from. In 18th century music it doesn't fit at all; composers often associated *particular* scales with particular moods, but the key centre mattered as much as the intervals in the scale (since it was both together that determined what kind of sounds you got from the instruments of the time). For Mozart, D minor is associated with dramatic action (as in Don Giovanni, where it predominated); G minor was predominantly gloomy and introspective; C minor had much the same associations as E flat, used for static and solemn ritual (as in The Magic Flute); E minor had the same uses as D and G, used for light dance music, the sort of thing that most easily fitted on the flute. A few composers used F minor for really dark stuff (like Haydn in his piano variations) but by the time you get to Beethoven, F major was generally dragged in along with it and you couldn't really tell which mode any nominally F minor piece was really in (just as Beethoven's Fifth is nominally in C minor, but he uses that the same dramatic-announcement way as Mozart before shifting into C major for most of the composition).