The pilot reported that en route on an instrument flight rules (IFR) flight plan in instrument meteorological conditions (IMC) the airplane began accumulating ice and shortly thereafter, he requested a "precautionary diversion" to the nearest airport to land. The pilot further reported that he exited IMC about 1,642 feet above ground level (agl) and circled over the diversion airport for landing. He reported that he had kept the flaps and landing gear retracted "to not adversely affect lift" and forgot to extend the landing gear prior to landing. However, when the airplane was over the runway threshold he reduced power, which caused the auto-extend function of the landing gear system to attempt to extend the landing gear. During the landing roll, the right main and nose landing gear collapsed. The airplane gradually slid off the runway to the right. The airplane sustained substantial damage to the right wing. The pilot reported that there were no preaccident mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation. In the Procedures section of the Piper Arrow II Pilot's Operating Manual, it states in part: Some aircraft are equipped with an airspeed-power sensing system (backup gear extender) which extends the landing gear under low airspeed-power conditions even though the pilot may not have selected gear down. For normal operation, the pilot should extend and retract the gear with the gear selector switch located on the instrument panel, just as he would if the backup gear extender system were not installed. The manual also states: The red gear warning light on the instrument panel and the horn operate simultaneously when: On aircraft equipped with the backup gear extender, when the system has lowered the landing gear and the gear selector switch is not in the down position and the throttle is not full open.