I have a kenmore refridgerator side by side. The freezer is beginning to have snow buildup (it is a self defrost) the refridgerator side is not cold

That snow is the condensate build up on the evaporator coils behind the rear panel of your freezer. Normally the freezer will go into defrost about every 10 hours and this snow will melt and drain out the defrost condensate line below the evaporator and go to a pan under your refrigerator and return back to the air inside your home. I believe your freezer is missing the defrost cycle either because the controls for the defrost are defective or the defrost heater and defrost thermostat is defective. I would be watching for an increase in refrigerator temperatures soon, due to loss of defrost. We will need to unplug and examine the evaporator coils behind the rear wall of the freezer. If frozen or covered with snow then defrost with a hair dryer and lets check the defrost heater and all its related components. Could you find a model number like 321.256489 for example then I can find the parts to look for. Sea Breeze