See my other comment. This can't be ruled out yet, particularly because the pilot seemingly climbed to get above the weather where it would've been colder and the air less dense, narrowing the operating window so turbulence or a sudden dive could've spun out of control.

Whatever the cause, it seems like climbing to avoid turbulence in or near thunderstorm conditions when the pilot knows there is ice already was probably unwise. A more prudent course was probably to divert around it and/or to descend to de-ice the plane. If so, would this rise to the level of pilot error? I don't know but maybe.