It looks bad for him to let your king in to f4 but your suggested 4.Nc5 was even stronger. So 3...Kf5 was more resilient and then White retains good winning chances after :
4. Nd8 Nf6?! 5. Nxc6 Ne4 6. h5 Nxg3 7. h6 Kg68. Kf4
So 4...Nb8 is necessary and it's probably drawn with best play.
7...Nd3 puts the knight on a losing circuit but it's a difficult defence anyway.
I reached this Knight Endgame in a OTB Tournament game. The position seems to be equal,but I wanted to win this game. My plan in this position is to win the black isolated pawn on the kingside and push my two connected past pawns to promote in to a queen.