I'm not a big app fan in general, one of the things I enjoy most about cycling is being disconnected from data. That being said, I do think some weather apps are great and that's all I need. Over time I've figured out which ones give me the best info for my little micro climate area of the world. I know what to wear if I know the weather. The apps I like are - Weather Bug elite, Wx Alert USA, and Accuweather. They're all good and together they make you feel like a meteorologist.
I've been commuting a long time, since way before apps and even before I had dial up internet in my home. I used to rely on the local TV weather report in the morning. I would get so annoyed by these "voice of doom" weather dorks that would always predict the worst possible scenarios every day which of course lead me to make poor clothing choices on countless occasions. Weather apps are my friend now.