With the knight on d3 White draws by Nf4+, hitting the king and heading for h3/h1; from d4 one square further away, the same pawn would win for Black. Knight endings are about exact squares, not general distance.
The black pawn on h3 is supported by the king on g2 and White's king is far away in the corner. Everything depends on whether the knight can reach the h-pawn's path in time, and here it just can: Nf4+ attacks the king, and from f4 the knight sees h3 (the pawn) and h5, g2, e2, d5 and so on. Whatever the black king does, the knight keeps checking or lands on h5/f2 squares controlling h1 and h3.