The symbols are generated by Yahoo weather.
Basically they are
Flat Clouds: Flat Clouds
White Dots: wear a coat
Droplets: bring an umbrella
Right now it's mostly sunny and cold. Friday, it will be sunny and less cold. Saturday, it will be rainy and snowy. Sunday will be warmer but still too cold. Monday: Not sure but it looks nasty. Tuesday: like Saturday only colder.
Seriously, the icons are dumb and the forecasts are usually wrong anyway.