Winters was involved again four minutes later when he sent in a long ball to the far post but Airdrie keeper Stephen Robertson got a hand to it before Kevin McKinlay could supply the finishing touch.
County were getting their act together and a slick move involving McKinlay and Winters set up Stuart Anderson with a chance but he blasted his shot well over.
The home side were playing with a strong wind at their back and some of their attacks were breaking down with the ball running out of play.
Winters had a chance to break through in the 24th minute when he latched on to a long ball form Sean Webb but he allowed himself to be dragged wide of goal and the chance was lost.
It was all County and Higgins, who had just recovered from a face knock, tried a long-range effort that Robertson gathered easily.
In Airdire's first real effort on goal a couple of minutes later Brian Twigg sent a weak shot wide of Joe Malin's right-hand post when a pass to a team-mate looked a better option.
Winters failed to control a throughball from Lionel Djebi-Zadi with only one defender to beat, then Higgins flashed a dipping shot over the crossbar for County's best effort.
A poor clearance from Robertson gifted Cowie with a chance but the County midfielder failed to test the County keeper from outside the area.
Willie McLaren was booked for a tackle on Higgins on the edge of the area, but the Airdrie wall took the sting out of John Rankin's free-kick.
The Diamonds made a bright start to the second and, after Brian Prunty hooked the ball wide of goal, Gary Twigg unleashed a low drive that just cleared the upright.
The visitors looked a different team with the elements in their favour and they took the lead in the 52nd minute when a Steven McKeown cross was headed in at the near post by Twigg.
At the other end, Robertson saved with his legs as Higgins raced clear on goal, but it was mostly Airdrie and Prunty came close with a backward header.
Airdrie were desperately unlucky in the 57th minute when a Stephen McKenna header came off the inside of the post and into the arms of Malin.
The game was dying a death with Airdrie quite content to hold on to their slender lead.
County came closest to an equaliser when a Rankin free-kick was fumbled by Robertson but the ball was eventually cleared.
Rankin forced a fingertip save from Robertson in the dying minutes as the home side went all out for an equaliser.