Is there a good reason to have a birdbath in winter? Absolutely there is!
Any backyard birder who has a birdbath will testify to the fact that it helps attract birds to their yard. Bird food does a great job of that too, but the yard with the birdbath will win the hearts of the local birds.
In winter this is no different. Actually in fact it may be all the more important. Birds eat food - seed and suet - to stay warm in the winter. The fat in the food ignites their internal furnaces and allows them to stay warm enough to survive. They have to eat A LOT to maintain this internal furnace. Water is still necessary for survival and in the dead cold of winter it can be darn near impossible to find a viable water source without expending precious calories that are so important to keeping warm and thereby surviving the harsh cold of winter.
A heated bird bath serves this purpose beautifully. Heated birdbaths fight the elements just enough to open a small enough patch of water that it serves the local bird population well. Our birdbaths here at the Birdhouse don't stay on 100% of the time, but cycles in and out with a built in thermostat making them energy efficient. They do require outdoor rated cords though as to not void the warranties.
And don't worry about the birds freezing their feathers. It would be very rare to see a bird bathing in colder temps. They're most likely to use it just for drinking. They're way smarter than most give them credit for!
Check out our heated birdbaths here.