Is this endgame winnable for White? Playing White against a computer, I reached this position (White to move):

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]


White has a queenside pawn majority, but Black's king is closer to the action, and its knight has the idea of Nd4-c2. I played this position through to the end about a dozen times, and usually only managed to draw: Black was able to pick up my queenside pawns, and even in lines where I got one of Black's kingside pawns in compensation, the position was still drawn. A couple of times I did manage to push the queenside pawns and win, but I didn't keep track of exactly what I did and it's possible the engine made a defensive error (it was set at a fairly easy level). So what should White's plan be in this position? Does White have a win here, or is this a draw?
EDITED ( January 7th, 2014 ):

Based on the member shivsky's comments I have edited the entire solution.




  Does White have a win here, or is this a draw?


Yes it is won for White. 


  So what should White's plan be in this position?


At first, I wanted to provide an answer with 1.a4 and simply force the win, but I do not have computer strong enough to analyze the variations I come up with, so my conclusions can not be 100% true.

I do not think that you can achieve much by creating the passed pawn immediately, at least my engine shows some convincing defensive lines.

And again you were right-even if you trade queen side pawns for his king side pawn, he might still draw.

My engine shows some lines where 1.a4 continuation allows you to get f7 pawn for your queen side pawns-giving White an advantage, but I strongly believe you can not win since all the pawns are at one side and Black's Knight can do a good job at defending and blocking.

Being strong endgame player, I must say that I do not like 1.a4 anyway.

ANSWER:

Your only chance is to deaden the position and to win by using your queen side pawns to distract his pieces from defending king side, when your pieces could invade there and get enough material to enforce queening. You need to start the action at the right moment. 

1.Kf1 can achieve that, when you could freely maneuver into the favorable setup which will create passed pawn and win. 

TO CLARIFY MY ANSWER:

I have tested this line with the engine to see if there is a valid defense, and engine could find none. 

I have tried to find one myself and 1. ...Nh4 was the best try I could find.

It is the only way to prevent White from activating his king ( if Black allows that then its game over ) and the idea is to harass White's King side pawns so Black could play f6 + g5 + Nf5 hoping to achieve something like this:

[fen "8/8/p3kp2/5npp/PPN4P/3K2P1/5P2/8 w - - 0 1"]

1. hxg5 fxg5


This would give him some counter-play ( he threatens to queen with h4 ) and would provide him a chance to exchange all king side pawns.Then he could try to catch the queen side pawn ( a6 pawn will 100% be exchanged for the b5-White has to play it at some point ) or to sacrifice the Knight for a pawn ensuring the draw. 

This is how I would try to save the game as Black, but White can refute this plan:

[fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

1.Kf1 Nh4 2.g3 Nf3 3.h4 Nh2+ 4.Ke2 Ng4 5.f3 Nh6 6.Ne3! 


This move restricts the Knight completely refuting the above plan.Without the ability to create counter-play Black is simply lost-White creates the queen side passed pawn distracting one or both of Backs pieces and then wins by taking all of Blacks pawns on the king side.

HOW TO EXACTLY WIN THIS:

First rule of endgames-king is extremely powerful piece-use it!

Second rule-of all the available moves that can implement your plan always play those that make the least commitment. This gives you the flexibility to adapt when position changes in its character drastically. 

The 1.a4 continuation breaks both rules, as it neglects the king and forces the matters-which unnecessarily sharpens the game and provides Black with counter-play based on his strong King.

In endgames you need to slow down the pace and see the whole picture. Raw calculation here is useless if you do not have a clear plan. 

To create a plan, we always start with the analysis of the position. Yours is sufficiently good for a start so let us go from there:


  White has a queenside pawn majority, but Black's king is closer to the action, and its knight has the idea of Nd4-c2. 


Third rule in endgames-in order to win, most of the time you will have to create at least two DISTANT weaknesses in the opponents camp ( if they are close then opponent might defend successfully ). Here we already have one-extra pawn on the queen side.

Our pawn structure is healthy-we have no pawn weaknesses on queen or king side ( doubled/isolated pawns... ).

The weakest piece in our setup is our king and that is our only weakness.

Our Knight is A MONSTER! This piece alone actually won this endgame! He is ideally posted-he can aid in creation of a passed pawn, he can attack on the queen side, he restricts the opposing Knight and King, he can harass the king side pawns if black king abandons them and he can defend our king side. WHAT A BEAUTIFUL PIECE! A HERO!

Now let us see what Black has:

Black's king IS active as you have correctly noticed, but he is badly placed-he needs to be closer to the center to balance the lack of a pawn at queen side ( e6 would be nice )-and that is something you have missed.

Black's knight is OK, he is posted well, but is decentralized which limits his actions-he can only attack on the king side at the moment.

Black has no pawn weaknesses, but is a pawn down. He also has started to probe the king side since h-pawn has advanced and can be supported with he knight and a king. He should try to create counter-play there, since he has no time to attack the queen side.

Let us see the entire picture:

Black's pieces are misplaced ( you missed this fact and this is important to notice ), they need 1 or 2 moves to centralize them selves ( they must do this in order to hold queen side ), and will spend even more moves to organize a defense/create counter attack.

This will give White enough time to activate his king.

Now we see the first phase of our plan-improve the king's position.

The second part should be about creating the second weakness-this type of endgame is well known and the usual plan is to create passed pawn on the queen side to distract king/knight/both and then to use our extra pieces to break through on the king side.

You saw what happens when Black tries to generate counter-play on the king side, now let us see what happens when he tries to centralize his pieces so he can attack on the queen side:

 [fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

 1.Kf1 Nd4 2.Ke1 Ke6 3.Kd2 Kd5 4.Kd3


At this point Black is in zugzwang, and no matter what he plays, White will simply parry his threats and eventually play a4 fulfilling the plan described above. Let us just see one sample continuation so you "get the feel": 

 [fen "8/5pp1/p4k2/5n1p/1PN5/P7/5PPP/6K1 w - - 0 1"]

 1.Kf1 Nd4 2.Ke1 Ke6 3.Kd2 Kd5 4.Kd3 Nc6 5.Ne3+ Ke5 6.Kc4 f5 7.a4 f4 8.Nd5 g5 9.Nc7 Nb8 10.b5 axb5+ 11.axb5 Kd6 12.b6 Kc6 13.Nd5 Nd7 14.Kd4 Nxb6 15.Nxb6 Kxb6 16.Ke5


And White wins. The queen side pawn majority did its job-it has distracted the knight, and eventually the king from defending the king side which was exploited with White's last move.

One thing I must mention is the usage of zugzwang. At certain point Black did manage to centralize his pieces, but so did White. At that moment everything boils down to small nuances and here it is White knight that saved the day-by restricting both king and knight he enabled the creation of zugzwang after which the creation of the passed pawn was easy.

Notice also, how the activity of the Black's pieces just wasn't good enough for a draw, since they were badly misplaced and notice how that gave White the time to improve his own king.

I think that this is enough for you to understand how to win this alone, so set up the position on your computer and try to win this time.

Good luck!

Best regards and a Happy New Year!