Part 91 pilot reported that during cruise; they encountered icing conditions and failed to turn on the pitot heat which caused the autopilot to disengage. The pilot lost control of aircraft and aggressively descended. The pilot eventually regained control of the aircraft and continued the flight.

Narrative

I was on an IFR flight plan with ZZZ Center and came across an icing situation. There was a a system moving west to east moving over ZZZ; and [I] was currently what I thought far enough east of the system while flying my route. While in the zone; I was monitoring my wings for collection of ice; but no collection. I was ready to ask for lower while looking at Foreflight flight planning; but I saw no icing accumulate on the wings. One thing I failed to do was to turn on pitot heat which caused an issue to start my fun. The pitot accumulated icing conditions and dropped the autopilot out; which started the airplane in an aggressive descent. The airplane probably lost up to 600' and I immediately notified ATC [that] I accumulated icing and was correcting for altitude loss. If I remember correctly; they gave me a lower altitude to get out of the icing; which it did.At this time; I started to incur moderate turbulence from the system moving west to east which made [it difficult] controlling aircraft straight and level. ATC gave me a heading to fly to get out of the turbulence but I still had to deal with the weather system. Airplane was difficult to hand-fly; as I was being tossed around losing/gaining altitude and speed. I discussed with ATC what was going on and just tried to maintain heading and altitude as best as I could. They asked if I needed assistance and told them no; I just needed to concentrate on flying the airplane. I was asked a couple times what heading to my destination and told them unable to give them the answer due to maintaining the airplane. ATC was awesome; working with me giving me heading and altitude changes which eventually led me out of harm's way which made me happy. I did what I thought was my research for the flight and continued to monitor weather progress during the flight. It was moving faster than expected which changed [the] course of my flight plan for sure. Bottom line: I did lose altitude more than is given for an IFR flight plan and lateral deviation but was in contact with ATC during this portion of the flight. I'm not saying I was 100% perfect in my execution; but I did get out of the mess and hopefully didn't cause too many issues for ATC.