Due to their innate bulk compared to earbuds, over-ear headphones aren't typically designed for exercise. They are more likely to move around on your head while running, for example, and for outdoor exercise in general, their isolating physical design could block out more external sound than is safe. That said, wireless pairs can be suitable fitness buddies, especially for use in the gym – though think about what your gym routine is. If you are doing weights in a horizontal position, over-ears are likely to slide around or, worse, slide off. We'd look out for ones that are lightweight, water resistant and preferably have a fit that clamps on the tighter side.
On-ear headphones would likely tick these boxes, though they aren't as common nowadays so choice is fairly limited.