After checking to make sure the scope mounts and rings are tight the most common reason for horizontal stringing is a stock bedding issue most particularily if there is contact between one side or the other in the forearm and secondly if the action is not squared in the bedding block. You can attempt to reset the action in the stock by loosening the action screws until you can move the barrel slightly then do this. Take some thin yet strong paper such as that found on the back of shipping lables and take a strip appx. 3 in. long x 1 1/2 in. wide and fold it over widthwise twice so you have a narrow strip 4 layers thick. Insert the paper strip under the very end of the barrel and slide it up into the very end of the forearm. If the paper will not fit try a 3 layer fold and insert again. Be sure to leave tag ends of the paper sticking out on both sides of the barrel above the top of the forearm for equal spacing. This done begin to slowly retighten the action screws until you feel them come to finger tight. At this point lightly bump the buttstock of the rifle a few times on the floor with the barrel pointing straight up and holding only the stock and never the barrel. Now is the time to remove the paper being very careful not to bump the barrel and tighten the action screws fully. Now check the spacing between the barrel and forearm using a good old dollar bill by draping it under the barrel and see if it slides nice and freeley up the barrel between it and the forearm. If you get a spot where it starts to bite then you have an issue with the stock. Of note there are some rifles designed with a pressure ring or screw in the forearm to purposely apply tension to the barrel. 2 schools of thought exist on standard probuction rifles, either free floating the barrel or applying tension to reduce barrel whip. Rule of thumb ( but not always ) is a properly floated barrel ( as discussed here ) is the better of the systems. DO NOT as stated earlier discount a cross breeze as the culprit but no breeze equals issue with the firearm. Hope this helps.

10 Spot