That's right, Jerry, they brumate. Mammals hibernate. Some estivate (summer). Brumating turtles have been known to slow their heartrates to one beat every ten minutes. The survive underwater for months by slowly pumping water into and out of their pharynx (throat) and cloaca (urogenital opening), which are lined with blood vessels and extract oxygen from the water much as a fish does with gills. They can even go completely anaerobic and buffer the accumulating lactic acid with calcium from their shells. They are truly remarkable critters.
My painted turtles go to the bottom of the pond and just become inactive, hiding under leaves and algae or between lily pots. I also put a u-shaped structure on the bottom that creates a low "cave" for them to crawl into. I've seen them become active in the winter and crawl along the bottom under the ice. The really impressive thing I've seen is turtles basking in the sun in January when we've had an occasional warm day. I've still not figured out how they know it's warm enough to come to the surface on a warm day. There are sunny days when it is cold, but they don't come out. With the temperature at the bottom of the pond relatively constant at 39 degrees, how do they know when it's warm enough to bask? They are amazing.
If you want to try to overwinter the turtle in your pond, make sure to keep a hole open to allow noxious gases to escape just as you would for your fish. In the wild, most turtles bury themselves in the mud at the bottom of the pond or at the edge. Painted turtles are much more resistant to the cold than are the red-ears. Obviously, painteds survive in northern Wisconsin and Minnesota. Winter is hazardous, though, to all of them. They must go into the winter in excellent condition or they will perish. I've lost turtles from time to time. The worst times for them are when there is an early warm period and they come out of their inactive state and then it gets very cold again. That seems to really stress them. You might try a container of sand for it to burrow into for the winter, but my experience with red-ears is they don't do well overwintering in a pond environment. I'd take it in for the winter or release it in its natural environment. People give me their unwanted red-ears from time to time. I have six right now that are going to Tennessee when I go to my brother's place next month. They'll make a good addition to his pond.