Webnorton shores, mi's climate averages. Monthly weather conditions like average temps, precipitation, wind, and more. Norton shores's yearly averages for humidity, fog, sun,. A 40 percent chance of snow showers. Cloudy, with a low around 28. North northwest wind around 13 mph. A 40 percent chance of snow. Webrain and snow in the evening. Winds wnw at 10 to 20 mph. Chance of precip 40%. Webnorton shores weather forecasts. Webclimate & weather averages in norton shores, michigan, usa. More clouds than sun. Webweather. com brings you the most accurate monthly weather forecast for norton shores, mi with average/record and high/low temperatures, precipitation and more.