A320 First Officer reported excessive wind noise on climbout. Investigation determined that they were flying in icing conditions and were experiencing erratic Air Data Information due to all three Pitot Tubes frozen. The flight crew performed Anti Icing procedures and continued to destination airport.

Narrative

Departed ZZZ at dusk; I was Pilot Monitoring (PM); climbing through stratus clouds or haze with light chop; TAT was above 10 Degrees C and E A/I was off through maybe FL180 and we noticed the wind noise in the cockpit was much more than typical. We thought this might just be a loud airplane.When we were at about FL216 I noticed our climb rate was zero and sometimes negative. There were tailwinds of approximately 50 kts. The Captain; also Pilot Flying (PF); selected speed from our current 320 kts. to 280 kts.. The aircraft initiated a climb but I don't recall climbing more than about 600 FPM and we didn't climb for long. Maybe a few hundred feet. I suggested to use vertical speed. The airspeed slowed as much as 260 kts. and we were climbing at a selected vertical speed up 1;200-1;500 FPM. I originally thought that we were having an auto flight problem; perhaps. I checked all the system pages and found them to be normal. The Engine Pressure Ratio was 1.34 I recall and thrust indication matched thrust lever angle cyan circles. At some point before this when the TAT reached 10 Degrees C; I had turned on the engine A/I. Both PFDs and the standby indicator matched airspeed indications. Finally; I had the idea to turn off the dome light and turn on the ice light and wing lights. I saw a large piece of clear ice on the ice indicator and it extended horizontally approximately 1 inch per side. The wings were somewhat hard to be sure but looked to have a good amount of clear but lumpy ice on them. I turned on the wing A/I after mentioning to the Captain.What I think happened was that the pitot tubes (all three) must have been frozen over and were no longer indicating accurate airspeed. Maybe the engine inlet sensors also as the Engine Pressure Ratio was lower than I would have expected and it increased some minutes after exiting the icing condition. I believe our airspeed was far higher than indicated as I've never heard wind noise that loud in the cockpit before. The plane seemed to not have enough power to maintain an altitude of FL 290 and had full power going Mach .78. After a few minutes the aircraft seemed to fly better and although Engine Pressure Ratio was now limited to I believe 1.44; the engines did not need to be at max thrust.This is a hard situation to fully understand because I'm not sure if the icing and its weight and drag were a larger factor or that I believe all three airspeed indicators might be iced over.