Whenever you play golf in the wind, conditions become far more challenging. The wind will not necessarily affect the ball on the green, although in very extreme conditions it can.
Usually with the golf ball being at ground level when you are putting it is under the wind and therefore not affected by it. However even though the ball is not affected by the wind, you will be when you are making your putting stroke. You will find that the wind will affect you by blowing you off balance and making your body move and sway during the putting stroke.
The best advice for coping with windy conditions when putting is to improve your stability and balance. Widen your putting stance to create a firmer base to play your stroke from. Widening your stance more than usual will also lower your centre of gravity more and having a lower centre of gravity will improve and make it easier for you to stay balanced in difficult conditions.
With improved balance you will sway less in the wind and as a result of this it will stabilize the swing of the putter. With the putter swinging in a more stable way, the putter head will travel on the target line more. If you are being blown off balance and swaying forward towards the ball, then the putter would swing off the target line to the far side of it. If you are being blown off balance and swaying backwards away from the golf ball, then the putter head will swing more on the inside of the target line.
In order to hit putts directly along your target line, you need to swing the putter head along the target line, with the putter face aiming directly along the target. If the putter head is swinging across the target line due to you swaying in the wind and being off balance, then it becomes much more difficult to strike the ball directly along the target line and to putt accurately.
Once you have widened your putting stance, work on shortening your putting stroke more than usual. The more that the putter is moving, the more chance it has to move off line in the wind. Shorten your putting stroke so that it has more opportunity to remain on the target line, whilst being swung. However, when you shorten your stroke, if your tempo remains the same the shorter stroke will produce a shorter putt. Ensure that you play a shorter stroke but hit the putt more firmly than usual to achieve the same distance.
If you work on widening your stance, shortening your stroke and striking slightly firmer than usual, then you should see that your putting is unaffected in windy conditions and that you adapt and cope to the more difficult conditions very successfully.