Simple endgame

3. Kf3! is definitely a subtle move, leading to an easy win. A couple notes to deepen the analysis:
(1) 1. Ke3 Kg4 2. Ke4 Kxh4 3. f5 also works, though just barely: 3.f5 Kg5 4. Ke5 h4 4. f6 h3 5. f7 h2 6. f8=Q h1=Q 7. Qg8+ Kh4 8. Qh8+ (skewers the white queen on h1) Kg3 9. Qxh1
(2) After 1.Kg3, white can still win because s/he can use the opposition to penetrate black's position, gain a pawn, and win the queening race. For example:
1. Kg3?! Ke4 2. f5 Kxf5 3. Kf3 Ke5 4. Ke3 and white's king will get to either d4 or f4 on the next move. I leave the continuation after that as an exercise to the interested kibitzer.