Do not be alarmed, there was probably nothing wrong with the cygnets. Swans (adults and cygnets) place one leg on their back in a resting position throughout the day as they are on the lake or pond. Some researchers think that this position not only serves as a resting position, but also a way to dissipate heat. The swan's foot has many capillaries and other blood vessels in the webbing. So, instead of panting like a dog to rid itself of body heat, the swan uses its foot as a means for this process.
The Regal Swan