My opponent and I had already been mumbling about a draw, but I insisted we play on for a couple more moves. Turns out that Black is winning, thanks to zugzwang! Once the pawns on the kingside are stuck, the White king will have to relinquish the protection of the c5-pawn. Black can then take the pawn and proceed into a winning endgame.
Lesson learned: if a situation looks hopelessly stuck and drawish, check again, and see if the position's got zugzwang.
Here are two illustrative positions from Bruce Pandolfini's Weapons of Chess:
In the first example, White is winning regardless of whose move it is; in the second example, whoever moves first wins.
