To be honest Tonydal, I don't think g4 gives white much of a chance either- white's king MUST move all the way over to the queenside, at which point black will pick his kingside apart!
who wins this pawn end game?
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Ok, sorry about my generalisations, I will give a sample line below, note that black's plan is to create a passed pawn on the queenside and use an h5 push at some point to destroy white's formation;
1. g4 (your suggestion) b5 2. Kf2 (white must stop the eventual passed pawn) a5 3. Ke2 b4 4. axb4 axb4 5. Kd3 h5 (to demolish white's kingside) 6. h3 (trying to maintain the structure) hxg4 7. hxg4 Kf6 8. Kc2 g5 and white has no way to stop both passers.
after 1 g4 h5 2 h3 hg 3 hg Kf6 with g5 coming I think black is winning the 2 to 1 majority on the qside is gonna be decisive , I believe black has more than one winning plan in the position , perhaps creating a passed pawn immediately on the q side is best with 1.... b5 followed by a5 and the white king will be forced to get inside the square of the soon to be passed pawn and the BK will enter the kside and fill his belly :-) Tony is right though that g4 is the only move that puts up any resistance as the BK cannot be allowed easy access to f5 and then e4 ..
White to move.