There is no general rule for multi-pawn endgames as they are much too complex.
However I believe that most of the pawn only endgames that appear in regular games are readily assessed correctly by grandmasters (or even just masters). Sure there are pawn endgame studies that might be tricky, but on average assessing a pawn endgame is much easier than an endgame with say rooks on the board.
In order to win a pawn endgame you have to promote a pawn (apart from rare situations where you mate with pawns only). So obviously one of the first thing to look for is the availability of passed pawns or the options for creating passed pawns. If there are, you would further assess the strength of those passed pawns: Can the king catch them? Are they protected? (This usually means that the king is bound to a certain part of the board and could be used for operations in another part of the board.) Do you perhaps have more than one passed pawn? If both players have passed pawns; whose pawn is quicker?, etc.
If there are no passed pawns, it means that (in order to win) you have to capture an enemy pawn with your king. Target pawns to be captured are often fairly clearly defined. Your opponent may defend passively, e.g. preventing you from getting close to the target pawn or he may actively try to capture one of your pawns and promote a pawn.
In situations like this, it is often essential to count correctly, make proper use of opposition and triangulation. Fortunately the number of possible moves is limited in pawn endgames, simplifying the calculation of long lines.
When assessing multi-pawn endgames, of course it helps if you know the rules of single pawn endgames (rule of square, rook-pawn,opposition, active king etc) since the multi-pawn endgame might turn into a single pawn endgame or effective single pawn endgames if pawn chains are blocked.