Start with the simple stuff first. Have you put in any fuel line deicer? Sometimes you can get a little water that pools in the low parts of the line and freezes when the weather gets cold. To check this possibility, use a little starting fluid next time the engine won't start and the weather is that cold. Spray some starting fluid into the air intake and see if you can get the engine to run for a few seconds on the starting fluid. If it will they you can know that the problem is related to fuel delivery. If everything runs great when the weather is a little warmer, it's probably ice in the fuel line. Good luck. Make sure the throttle plate is closing enough to allow proper choking for cold weather start.