You just described Auckland weather on a good day
Wake up to a freezing morning. Within minutes the suns out shining, but the wind is blowing like crazy making the chill factor worse then some places where it snows. You dress warm, start walking to work/school. 5 minutes into the walk, you have to remove the jacket etc, as the sun is now beating down 22 degrees with no wind. 5 minutes from school/work it starts pouring down with heavy rain, stopping just as you get inside. Repeat every time you are outside.