C140 pilot reported the engine lost power while applying full throttle for a climb and could not be restarted. Pilot conducted a safe off-airport landing. Post-flight; it was determined that carburetor ice was the likely cause of power loss.

Narrative

Cessna 140 departed ZZZ with two occupants. The flight plan was to do air work in the area NNE of ZZZ bounded roughly by ZZZ1 and ZZZ2. After climbing to approximately 2200 feet MSL we practiced turns; dutch rolls and coordination exercises for about 25 minutes at 2200+/-100 MSL and groundspeed between 80 and 100 MPH per ADS-B tracking. At this time ZZZ2 winds were 6 MPH; Temp 69F and Dewpoint 58F for RH 68%. Engine RPMs were approximately 2200; consistent with these speeds and level flight. No engine roughness or loss of power was observed. Airspeed and altitude were maintained without noticeable changes in throttle or retrimming/loss of airspeed. About [30 minutes in to flight] we were near the dragstrip on a roughly NW heading and decided to climb to 3000 ft. When the throttle was advanced power was substantially or totally lost. Power loss occurred when the throttle was advanced; not prior to or after throttle advance and a power loss; not merely a failure to increase was observed. No sputtering; backfiring; roughness; surging or any engine change except a loss of power was observed.The aircraft had an annual signed off the day before and as part of that annual the throttle linkage end link had been upgraded from a ball and socket style to a rod end style per Cessna SE79-6. The throttle seemed to be disconnected with no response over the full range from idle to full. This motion was repeated several times to confirm. The failure to respond led me to conclude the throttle had failed in some way associated with the maintenance and I began a descent at about 65 MPH and 600 FPM and turned N toward the dragstrip. At this point I began the engine out checklist with fuel (tank; mixture and CH (carb heat)) and then checked the mags. These checks had no noticeable effect. The engine seemed to be operating at either idle; very low power or windmilling. Based on the fact that it stopped on roll out I believe that it was windmilling at this time.At this point we were at approx. 1;500 feet MSL/1;300 feet AGL and I decided that the field was preferable to the dragstrip being less obstructed and we began a 180 turn to reach the field. At the end of this turn we were at about 500 ft. and well above standard glidepath and began slipping to reach the field and not overrun it. During this turn we contacted ZZZ Tower; which was the last frequency set in our comm radio; though we were well outside their airspace. At no point during this descent and turn did the engine make any noises indicating an attempt/willingness to restart. After the first diagnostic attempt and after choosing the field as target no more attempts to troubleshoot or restart were made. The engine continued to windmill and the prop was never stopped.We touched down approximately ½ way through the field and rolled out without hard braking. The engine was dead on rollout. We attempted to contact ZZZ when on the ground and were unable and then managed to make a weak connection on 121.5 to an aircraft and requested relay of message but didn't hear if this actually got through. Then managed to google ZZZ Tower telephone and made cell call. Soon after the authorities arrived and we made provisions to secure the aircraft. Before leaving that night I tested for fuel flow at the gascolator in the as-landed state and got fuel flow.The following day the engine controls (throttle; mix; CH) were determined to be operational. Fuel flowed to gascolator. The aircraft left ZZZ with 9.5 and 10 Gals (L/R) and on the ground had 7.25 and 9.5. These measurements are based on a calibrated stick and approximate. Tanks were sumped and no water observed; fuel blue. The aircraft had been fueled in the morning and flown 1.3 hours before this flight; on both tanks. This flight had a Hobbs duration 0.8. The first 30-35 mins were run on left tank; the last several minutes before the failure on the right tank. Fuel flow was observed to gascolator from both tanks. Gascolator screen appeared clean. Oil level 3 3/8 qts. No damage or evidence of bird strike or obstruction on aircleaner. The engine was then started; warmed up and run up with no issues. Static run up was ok.[Later] the aircraft was inspected by an A&P/IA and these checks were repeated. Compression was observed on all cylinders; the magnetos were checked and the gascolator screen; carb inlet screen were checked and cleaned with no obstructions found. The carb bowl was drained and flushed. Fuel flow from both tanks to the bowl was confirmed. The carb inlet was checked and boroscoped with no problems found. The engine was again started and run up; passing all tests. Having eliminated all mechanical possibilities; the aircraft was signed off and was flown out of the field and back to ZZZ.I believe we were operating at all times within the POH and standard practice; at least as I was instructed. My instruction was CH on descent and when RPM <2;000; and when icing is observed. The Cessna 140 POH lists 2;100 RPM as a cruise setting and does not call for CH during cruise. We flew extensively prior to losing power at constant altitude and generally constant airspeed (discounting variations due to maneuvering). This profile in this airplane requires about 2;200 RPM and this is where we were operating for the 20+ minutes prior to losing power. The Cessna 140 POH is not very detailed; but the Cessna 150 has essentially the same engine (O-200 vs C-85) and its POH has similar guidance. It does not call for CH for cruise flight unless symptoms noted and cruise flight is listed as 2;000-2;750 RPM (which corresponds to the green tach arc). The FAA knowledge test and PHAK identify below 70F and high humidity (80%) thus we were operating (68F and 70%) just inside or on the boundary. Conditions at altitude would be more conducive to carb icing of course. Flying in the northeast one rarely flies outside the 'icing' zone on the standard temp/dewpoint chart.However; the only conclusion is that we did encounter carb icing with no symptoms. We did not notice any engine roughness prior to loss of power; nor does the flight path indicate a loss of power through either descent or loss of airspeed that was not detected in the cockpit. Given that we did have carb icing; had we detected symptoms and followed the Cessna 150 POH guidance 'to clear the ice' we would have 'applied full throttle and pulled the CH knob fully out'. This is what we inadvertently did when we opened the throttle to climb. This killed the engine. Had we then immediately applied CH it is possible that sufficient heat existed to clear the problem; however the C-85 has straight exhaust pipes and low thermal mass. The time delay between the failure required to establish glide; find a preliminary landing spot and confirm that there was in fact a problem was probably 15 seconds; during which the exhaust may have cooled sufficiently that no carb heat was available and no recovery of power possible. The checklist checks were performed quickly; but given that an acceptable landing spot had been identified I believe the proper course of action was to cease attempts to fix the issue and focus on a successful landing.