I feel trapped by my hair-washing schedule, particularly because it takes forever to dry, and looks terrible until it's completely dry.
Sometimes I don't want to workout because my hair is clean
^ This is EXACTLY how I feel! My hair is my security blanket so I can't wait for the day that I have enough guts to cut some of it off.

I'd say just go for it but don't go too short. Spring is a great time for a change like that. Kind of like "Spring Cleaning"

Good luck!