The pilot reported that while practicing ground reference maneuvers the airplane's engine had what he described as a temporary partial loss of power. The pilot was flying back to the airport when the nose landing gear struck a power line. The pilot continued the flight back to the airport. When he attempted to land, the nose landing gear collapsed aft, substantially damaging the firewall. While review of the carburetor icing probability chart revealed that the weather conditions during the flight--a temperature of 26 degrees Celsius and a dew point of 6 degrees Celsius--were conducive to light icing during glide and cruise power, the investigation was unable to determine a cause for the reported power loss.