The pilot and pilot rated passenger (right seat) departed in the PA-23 and climbed to 11,000 feet on a local round robin flight. The aircraft was not equipped with wing or propeller deice/anti-ice systems. Missoula reported several scattered, broken and overcast cloud layers below 11,000 feet during the afternoon and the surface temperature peaked at 44 degrees F. At 11,000 feet the pilots encountered a vibration and loss of left engine power and initiated a return to Missoula for landing. Unable to maintain altitude with partial power, a forced landing was executed short of runway 25 at the Missoula airport. Although an attempt was made to lower the landing gear prior to the forced landing, the nose landing gear collapsed during rollout when it struck a gopher hole. Airport ARFF personnel observed ice detaching from the aircraft wing(s) following the accident and FAA personnel inspecting the aircraft subsequent to the accident reported that the left induction air filter was heavily soaked with water.