1...Kh4, 1...Kh6, 1...Kg6 should all lead to a draw.
1...g4 loses outright, of course. After 2.fxg4+, 2...Kh4 loses to 3.Kf3. For if 3...Kxh3, then 4,g5 Kh4 5.Kxf4 Kh5 6.Kf5 and the pawn will queen. If instead of 3...Kxh3 black tries 3...Kg5, then white can play 4. h4+, with similar results.