Are there rules for categorising all pawn-only endgames into won/drawn/lost? If a situation containing only pawns and kings is displayed is there a simple set of rules for determining if the position is won/drawn/lost?

I know for single pawn and double pawn endgames this is true with rules like the opposition, rule of square, rook pawns etc.  My question is, does this extend into multipawn games or are they simply too complex and varied?

Another way of putting the question might be: if you show two grandmasters a pawn only endgame; do they both immediately know the outcome, or are there some that they would need to play out?
Generally speaking, the side with the most pawns will win. The tempo provided by the extra pawn is usually enough to gain opposition and access to the key squares. Doubled pawns don't matter for this, unless they're blocked. The extra pawn can also limit the movement of the opponent's king, resulting in the possibility of a triangulation maneuver.

Another recurring theme/rule is the breakthrough. Grandmasters know the patterns for which a breakthrough is possible by heart.

But generally, multi-pawn endgames are just as complicated as other endgames. There is a Russian endgame study composer, Nikolai Grigoriev, who is famous for his pawn endgame studies. They truly show the rich possibilities of chess with just kings and pawns. With so many beautiful studies available, you know that there can be no general rule to determine the outcome.