The pilot in the tailwheel-equipped airplane reported that during a banner towing operation, the ground crew attempted to connect the banner to the hook, but the banner did not connect and became affixed to the tailwheel. The pilot made several approaches over the banner field to dislodge the banner. He reported that during his last attempt to dislodge the banner, he moved the throttle to idle and made a normal descent to drop the banner. The banner remained affixed to the tailwheel, and he stopped his descent, and then he moved the throttle from idle to full power. The engine sputtered with no increase in engine power. He then visually and physically confirmed that the mixture was in the full rich position, and that the primer was in the closed and locked position. He attempted two more iterations of moving the throttle from idle to full power, with no subsequent change to engine power. The pilot made a forced landing on the southwest corner of the field, and the airplane collided with uneven terrain and trees. The airplane sustained substantial to both wings and the fuselage. The pilot reported that there were no mechanical malfunctions or failures with the airplane that would have precluded normal operation. The pilot reported that the temperature about the time of the accident was 80°F. The METAR at the nearest airport reported that the dew point about the time of the accident was 72°F. The relative humidity was about 77 percent. During a post-accident interview, the pilot reported that he did not use carburetor heat during the banner towing operation. He reported that during the multiple patterns to release the banner, carburetor heat was not used during the low power setting approaches to release the banner. According to the FAA Special Airworthiness Information Bulletin CE-09-35, the use of carburetor heat is recommended when operating in conditions of visible moisture or high humidity, while on approach with low power settings. The FAA Carburetor Icing Probability Chart shows that when operating at idle, with the above-mentioned atmospheric conditions, that the likelihood for carburetor icing specified a serious icing probability.