Just because you say so? A right requires no permission. Swimming in a public pool is not a right since it requires prior permission and can be revoked. The mere fact that public pools are closed in winter months is an indication that swimming in them is a privilege granted by the municipality that built the pool.
No, because the public has decided to establish such rights.
You see, Demidog, the public owns its public pools and its members enjoy rights attendant to that ownership.