Is it ok to go swimming with a cut on your face?

Not best choice: Depending on severity of the cut and its state of healing, swimming in a freshly-chlorinated pool may be safe, but still irritating (and thereby potentially more scarring) for a not-yet-sealed cut. In a dirty pool, hot tub, or river/lake/ocean there are many nasty bacteria that could potentially cause an infection and a much worse problem and scar. Wait until healed, and use a high spf sunscreen!