There is a possible winning plan for White if he can play h4-h5 gxh5 Kxh5 then Kh6, Bg7 and g4-g5-g6 because the King gets to f6. But I think White can't achieve this if Black plays accurately.
But now Be5 seems to add biiiig winning chances. gxh5 is proly the only move, but then your guys plan seems to work, Kh5-->Kh6 (make him play Kg8) and then g4 - g5 - Bg7 - g6
But now Be5 seems to add biiiig winning chances. gxh5 is proly the only move, but then your guys plan seems to work, Kh5-->Kh6 (make him play Kg8) and then g4 - g5 - Bg7 - g6
I guess it's still a draw though, Be5 Bb5 Kh6 gxh5 Kxh5 Bd3 seems to be good enough.