I agree that it could be caused by having a non vented petrol cap fitted. Several years ago when it was very cold I had a similar problem and I my assumption is that I had ice form and block the vent path. When I took the cap off I could hear the air rushing into the tank and the engine started up once again.

I will attached a picture of a locking type cap stripped down so that you can see the vent path. There is no hole to see, there is a slot cut under the rubber seal and up the side. Very crafty. If you look carefully with the rubber seal in position you can see the slot up the side.