A319 Captain reported a loss of control while approaching the gate in freezing rain conditions. After the aircraft slid forward a few feet; the flight crew decided to shut down the engines; stop the aircraft; and be towed in to the gate.

Narrative

Field Conditions reports; five; five; five; for Runway XX Left. All taxiways and Ramp areas were reported slippery. Light freezing rain. We started the APU just after touchdown. We taxied very; very; very; very slow with both engines running. Breaking action on the runway was good; and the taxiways for us until this point was good. We approached the gate area at the top of the tee - wide open area - with idle thrust; at the slowest possible taxi speed. Wide open area; no obstructions. Testing the braking action; I pressed on the brake pedals with full pressure. The airplane continued to slide forward for approximately 3 or 4 feet. I asked my copilot to shut down both engines immediately; to kill any forward thrust being produced; APU on. The airplane came to a stop. Parking brake was set. We called Operations and told them that we wanted to be towed in. They said no problem. They also said that they were going to treat the gate area first - more grip. My question is; why they didn't treat the lead-in line prior to our arrival? The tow in and parking checklist was completed without any problems. I completed a postflight walkaround; mainly to check out the conditions; and it was like an ice skating rink...While airborne; we briefed what we would do if the airplane would not come to a stop on the taxiways. I am glad we started the APU early.