B767 First Officer reported a wing anti-ice system malfunction during climbout in icing conditions. The crew returned to the departure airport and landed.

Narrative

I was relief pilot for this departure. I read through the new ATIS as we sat getting de-iced. In the ATIS; I read that a 757 had reported icing in the climb. We discussed this and discussed the use of wing anti-ice after thrust reduction. We taxied for takeoff uneventfully. At thrust reduction; we once again discussed using wing anti ice and turned it on. We immediately got a L WING ANTI-ICE EICAS message as well as overhead light. At this point; we were fluctuating between 10-11 C on the total air temperature (TAT). I pulled up the QRH as we climbed to 6000 feet. Since TAT was 10C; we decided not to go higher. We finished the QRH; which stated not to fly into icing conditions. Unfortunately; there was icing all around and this was not possible. We were overweight by about 40;000 lbs; but not knowing if we would start picking up icing and having nowhere to go to get out of the icing; we elected to return to ZZZ as soon as possible and get on the ground. I tuned and identified the ILS to XXR; as we wanted to land on the longer runway. The Captain and First Officer (FO) set up for the approach and discussed the overweight landing and ran the overweight landing checklist; and I briefed the flight attendants on the return to the field and called operations to tell them we were coming back and tell Dispatch. The flight attendant stated that they did not currently see ice accrual on the wing. On the descent; the TAT dropped to 3C. Initially; we did not pick any icing up; but in the descent; we began to pick up icing on the wipers. The First Officer (FO) stated it was less than a quarter inch; but clearly visible. We flew the approach. When placing the gear down; it took longer than normal to come down; leading to a gear disagree at first. Luckily; the gear came down and we continued on the approach uneventfully. When the Captain clicked off the Autopilot; he stated the controls felt mushy. He stated he had the runway in sight and landed firmly in the first 1000 feet of the runway. We turned off the runway. As we were taxing; we saw that the brake temperatures had now reached as high as 7 for the Brake Temperature Monitoring System (BTMS) value. I pulled out the QRH for hot brakes and we stopped in the ramp area to run the checklist. The brakes eventually cooled as directed; and the fire personnel stated they did not see smoking. We taxied into the gate following the guidance of the checklist and shut down.