Swans usually are not easily domesticated, but this is an individual attribute if they like and trust you to the point of touching. You may need to build further trust before they allow you touch them, but again, this is an individual attribute.

As far as the winter, if the pond freezes, you must place a de-icer in the pond or bring the swans indoors for the winter. Predators can access the ice and attack the swans, the swans could drown if they fall through the ice, or starve, become dehydrated or more susceptible to illnesses if the weather is too severe.

As far as the island, you do not want the swans anywhere near a stone island. The swans can easily injure their feet and legs to the point that they could become so injured that they cannot enter or exit the water which may cause death. The abrasiveness of the stones can also cause a condition known as bumble foot caused by injuries that lead to a staph infection. The bumble foot can become so severe that the swans will not be able to enter or exit the water by climbing up and down the bank, again possibly causing severe injury or death from inability to access water and food. The Regal Swan