Make sure none of the water from the icemaker has made its way to the coils however since you described the ice as snow I assume you have a defrost issue. There are four things that can cause this and they are the defrost heater, defrost thermostat, evaporator thermistor and the main board. The heater is the most common followed by the thermistor. Check the heater first you can remove it and check it with an ohmmeter if it is open or very high ohms replace it (should be around 25-40 ohms).

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Refrigerator Defrost Problem Diagnostics


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Your icemaker problem may be due to the water valve running too much water overflowing the icemaker sometimes the icemaker can cause this too. Sometimes water will leak over the edge (not due to overflowing) for various reasons. This can be solved using rtv under the cube separator on the edge of the cube form. Remove the cube separator and put a bead of rtv near where the water enters the icemaker. If the water comes in on the side of the icemaker put the rtv on the edge directly across from the water entrance.