Ice Maker Supply Tube is Freezing Up?

This sounds like a problem due to weak water pressure. If your fridge has a door water dispenser try holding a cup under it and see how fast the water comes out. If it comes out slow or not at all then pull out the fridge, turn off the water supply, unhook the water supply from the fridge and hold the tube into a bucket or large container. Turn the water supply back on and see if the water has a strong steady flow. If it does not, then it is freezing up due to weak water pressure and the problem lies further than the ice maker. Do not forget to thaw the ice maker lines once your fix the water pressure problem.