Guess what? Sunburns on cloudy days are a thing. This is a bad news/good news situation...
The bad news - you can get sun burned on a cloudy day. Clouds can block some UV radiation, but UV protection varies based on clouds' thickness, density and composition. Your UV exposure will also depend on the time of day, your altitude & your location. Bottom line - up to 80% of UV rays can penetrate clouds, even on an overcast day.
The good news - quality sunscreen (look for one with SPF 30 or higher - this is our favorite) and a good sun shirt will protect you with minimal effort.
Bottom line - sun safety is a year-round commitment. Build easy, daily habits for a lifetime of healthy skin.