Cirrus Vision SF50 pilot reported that during cruise the aircraft trim system malfunctioned. Reporter stated when the autopilot was disengaged; the aircraft nose pitched up and the trim wheel was difficult to move. Pilot performed a successful diversion and stated that ice on control surfaces could have contributed to the event.

Narrative

It was raining in ZZZ when I departed; temperature around 13 degrees C. After takeoff I climbed through some rain clouds; light turbulence at best; and I noticed the temperature dropped down to 6 degrees C quick so I turned on the Engine IPS and monitored the wing/windshield for ice. I did not get any airframe icing at all. Above 10;000 and all the way to FL310 it was clear skies; no issues or signs of anything wrong during the climb. I verified that it pitched down and leveled off at the assigned altitude; performed checklist and checked fuel planning before I engaged in conversations with my passengers. Maybe 3-5 minutes into cruise flight I got an altitude alert and looked to see that I was 200 feet high; and initially I thought maybe Alt didn't capture on the autopilot so I selected VS and scrolled down and nothing happened. After a second of head scratching I clicked the autopilot off to hand fly it back to FL310 and the nose pitched aggressively up; when I tried to trim nose down that's when I discovered I couldn't hardly move the trim wheel at all; maybe a half inch either way and it stopped. I went flew back to FL310 and went through maybe 200 feet below before I finally figured out the control pressure and still fighting the trim wheel. ATC didn't say anything about my altitude deviation but without the autopilot I asked to descend out of RVSM airspace. I communicated with my passengers and assessed my location; and decided that instead of going to my original planned destination of ZZZ1 for fuel; I would go to the adjacent ZZZ2 just in case it wasn't icing on the controls like I suspected and ended up grounded the aircraft at in ZZZ2 so that my passengers could still catch airline flights to their homes; which they were able to.I think the rapid drop in temperature on an already wet soaked airplane froze the pitch trim tab hinges; or some part of the control input.I could have deviated around the weather possibly but it was light rain showers and again hardly any turbulence so I didn't think it was unsafe to fly through the rain cells. Maybe spend a little extra time monitoring the instruments after the level off as well.