Hi Arctic,
Sure---go for a swim and enjoy the summer weather and your hair piece. You can do anything in your unit including amusement park rides, jogging, tennis, etc. Just make sure you have a strong attachment---that's the key. Use a good tape like 'Walker No Shine' or a strong glue like 'Ultra Hold' (or a combination of both). When sweating some people just rinse the hair with plain water and others shampoo the hair--it's your choice.
Regards,
John