SR20 instructor pilot reports landing with locked brake causing aircraft to contact a snow bank and depart the runway.

Narrative

Departed on a training flight to do practice pattern work and landings. Flight Instructor took controls over the field to check wind and runway conditions. Entered the traffic pattern and made a normal approach. Upon landing the aircraft fish-tailed and felt like it was on ice so I stayed off the brakes to keep the airplane straight. The airplane rolled straight for a short distance then veered to the left. I tried to correct by applying right rudder but was unsuccessful. The left wheel hit the plowed snow on the side of the runway and made the aircraft slide sideways. The aircraft then proceeded off the side of the runway and into the snow. The engine was shut down and fuel shut off. The Cirrus airframe parachute system pin was inserted and then I exited the aircraft to verify any damage. No major damage was found just a scrape on the wing where the plane hit a runway light. After exiting the plane and looking at the runway the preliminary thought of the cause was a stuck left brake; which caused the airplane to veer to the left. To prevent this occurring again a more firm touchdown may be needed to break the ice from the brakes and wheels free.