If there is a male, she is not going to lay eggs just to be laying in the winter. So, they could very well be fertile. If you move her, you will certainly kill the eggs. We would keep her in the barn until the last cygnet hatches. Keep watching the eggs. Cygnets will usually hatch in order, first egg laid, second, etc. So, once a hatching occurs, the next should happen within 1-2 days. With 3 eggs, this process should occur in that time frame. Form a nest in a safe area using straw on or near the pond, among reeds preferably because predators will kill them on the bank and there still are no guarantees. But, the mother needs an area to bring the cygnets on land at night and get them in the water for feeding during the daytime. Make sure this is a zero entrance area because a steep area may hurt the delicate feet and legs which could be life threatening. Also, steepness may cause the cygnets to drown if they can't climb out of the water.

Once all cygnets hatch, wait 24 hours after the last hatching, then take the entire family to the straw area. You will need to carefully grab the cygnets so the mother does not step on the cygnets while trying to protect them. You will need help so that the parents get off the nest so you can grab the cygnets. Gently, control the parents' wings and then wrap them in a blanket. Place the cygnets in a towel lined container so they are not on a slick surface, pick up the cygnets easily as you can strain their legs and that would not be good. Carry the whole family at the same time to the straw area. Place the cygnets on the
straw, then release the parents about 5 feet away. The parents will run to the cygnets and take them into the pond.

If you can catch the cygnets, and the parents immediately follow, you may not need to carry the parents, but it would be safer for all concerned. Again, just be careful with legs and wings so you nor the swans get jnjured. Regal Swan