We present a scanning force microscope that operates in a dilution refrigerator at temperatures of about 100 mK. We use tuning fork sensors for scanning gate experiments on mesoscopic semiconductor nanostructures. Slip-stick motors allow sample coarse-positioning at base temperature. The construction, thermal anchoring, and a procedure to optimize the settings of the phase-locked loop that we use for sensor control are discussed in detail. We present low-temperature topographic and scanning gate images as examples of successful operation.