k7/7p/4p2P/4P2P/1p2P3/1Pp5/2P5/N6K w - - 0 1
Thank you for sharing Alena, I came to a similar conclusion after the second cup of coffee it all hinges on white being able to get to f6 before white can capture the e4 pawn on the kingside or as you point out d3 if black is on c5 I will get back to it after I dig myself out of the snow and move my car.
If white wants to win then the white king must occupy d3 or g5. Therefore the black king mustn't allow to occupy these key squares. If the white king is on d3 then the black king must be on c5. If the white king is on g5 then the black king must be on e7. White can win with the right maneuvering.
Black fails to occupy c5 on time that's why black loses. If white moves Kg2 or Kh2 black manages to ocuppy key squares on time to get a draw.
After 3.Kf3 black most likely will not move 3..Kc5 but 3..Kc7 so back to the drawing board, tomorrow is another day.
I am just looking at the position again this is one variation 1.Kg1-Ka7 2.Kf2-Kb6 3.Kf3-Kc5 4.Ke3-Kb5 5.Kf4- Kc5 6.Kg5-Kd4 7.Kf6-Kxe4 8.Kxe6 looks good
I must admit I am really tempted to look at Alenas solution( lol) but then I would not get any satisfaction or gain any knowledge so plod on I must till later Russ