What temp was it running at last? You are right to think you will be running lean, but I think that there other things in it to consider. Where is your mixture screw? If you have it out 1 1/2 turns or more you can make the adjustment there. If you are in too far already then, you would have to fatten the jet one size, but it would have to be extreme differences to think you would need to fatten by two. How has the plug color been at current setting with warmer temps?
I believe needle setting should stay the same, unless it hits too hard to ride. It basically controls throttle response IMO.
I would turn the screw in one full turn and start it up and ride it at that temp to see how close you are. The safe thing to do is to refer to jetting chart and apply your temp and elevation and compare to what you have. If your k5 is bone stock, it should tell you exactly on jetting, needle and mixture screw and it will run like a new one.
It will probably be easier to ride if you gear down some on ice and snow. Ride on the grunt power.
