Freezers often have thermostats separate from the fridge to control how cold it gets inside. The thermostat is usually controlled by a numbered dial. The higher the number on the setting, the colder the freezer gets in response. Most freezers should stay in the middle range of the thermostat for optimal operation. Turning the thermostat up all the way results in a colder unit that may freeze your water supply line and unnecessarily wastes energy. If the water line is frozen, check the thermostat first, then either turn the thermostat down or unplug the freezer entirely to let it defrost.
Many freezers regulate their own thaw cycles to prevent a potentially damaging freeze. They rely on a timer that shuts the system down in regular intervals so that ice never has a chance to accumulate. If the defrost timer malfunctions, the freezer never shuts off and the water line gets no chance to warm up as a result. This is temporarily solved by unplugging the freezer to thaw the fridge manually, but if the problem continues, the defrost system needs inspection and possible replacement.
Moving water freezes much more slowly than standing water. The water in your water supply line should flow at enough of a pace to prevent ice crystals from forming, but the water movement can get interrupted. A kink in the supply line would result in diminished water flow, and freezing elsewhere in the system could contribute to the problem as well. As water starts to freeze, it expands and forms a blockage that prevents water from flowing past it. As a result, ice forms and spreads up the supply line until the whole line is frozen.
Inspect your freezer every few days to ensure ice is not starting to build up inside it. Keep the thermostat in the middle-range. Clean the coils of your fridge regularly. Dust buildup on the coils interferes with proper function, and the cold air can't travel as effectively through the system, which sometimes results in ice formation. Ensure that the drainage system doesn't get clogged, because that results in standing water that freezes. Clean the drain with vinegar if you suspect a clog is forming.