Overwintering Kent Beauty Oregano

Will the stems and leaves go dead or brown looking even in the house for winter. I'm assuming the plant would go dormant outside in winter. Will it go into a dormant time in the house too?

Oreganos seem to slow down during the cooler indoor temperatures in a house, but they do not die down unless they are frozen. If the freezing comes too suddenly, that is if the plants have not experienced close to freezing temperatures for several nights, then the sudden freezing will kill the entire plant.