PA32RT pilot reported loss of pitot heat and flight instrument indications in icing conditions. Pilot diverted and upon landing had a temporary loss of aircraft control.

Narrative

I filed an IFR flight plan from ZZZ to ZZZ1. As part of the preflight I checked the pitot heat was operational as I knew I would be climbing through a thin layer to 4000 feet and it was hot. About an hour and fifteen minutes into the flight we entered some light IMC and noticed my airspeed indicator was jumping around at about 0 degrees Celsius. I requested lower to get to warmer temperatures and as I descended the temperature didn't change and the airspeed kept lowering to 60 knots and then to 0 knots indicated airspeed although the manifold pressure and rpm were correct for the descent. The groundspeed on the GPS was also correct. The altitude indicator was erratic. The attitude indicator on the Aspen E1000 suddenly turned 90 degrees to the left however; the backup gyro/vacuum driven attitude indicator did not. I was without airspeed and altitude indications in IMC. I radioed to [request priority handling] but I don't know if that was ever heard as after several attempts; I did not receive a response. I switched to the alternate static source and continued a slow descent until I broke through the layer at about 1500 feet. I was then contacted by an aircraft relaying a message from ATC. I reported to them that I was circling to land at ZZZ2. Upon changing frequencies and locating the airport I radioed on XXX.XX that I was entering downwind; base and final. Upon landing the runway had about 4 inches of slush and a quartering; gusting headwind that continued to push the aircraft sideways. Without any traction and with full rudder and aileron I was unable to keep the aircraft on the runway; striking a runway light before regaining control and taxiing to the FBO. Once in the hangar; I tested the pitot heat again. There was no voltage drop and no heat on the pitot tube. I believe the pitot heat failed during flight causing it to ice up and also causing the failure of other flight instruments.