Can I keep a dahlia in a pot in the house over the winter?

You can bring it in, but I don't expect it to flourish and bloom indoors because of the dry air and short days. After a frost kills the top, let it sit for a day or two to allow the moisture to drain into the tubers. Then cut off the dead stuff, but leave a bit of stem attached. You can bring the entire pot indoors, into a cool, dark area. Only water occasionally during the winter to keep it from becoming bone dry. Better yet, you could unpot it and shake off the soil and let it dry. Then put it in a paper bag in a cool, dark place. The idea is to keep it dormant until it can go outdoors next spring. Check it about once a month in winter, and if it seems too dry, soak it in a pail of water for a few minutes and then let it dry again.