The pilot-in-command’s approach to the critical angle of attack during initial climb, which resulted in a vibration the flight crew improperly identified as an engine issue and resulted in the subsequent off-airport landing. Contributing to the accident was the operator’s inadequate and contradictory guidance for flight crews operating in winter conditions. Also contributing was the pilot-in-command’s decision not to perform a tactile check or deice, which resulted in taking off with ice contamination.