We present studies of the magnetic domain structure of UMn$_2$Ge$_2$ single crystals using a home-built low temperature magnetic force microscope. The material has two distinct magnetic ordering temperatures, originating from the Mn and U moments. At room temperature, where the Mn moments dominate, there are flower-like domain patterns similar to those observed in uniaxial ferromagnets. After exposing the sample to a one-tesla magnetic field near 40 K, the evolution of the magnetic domains are imaged through zero-field warming up to 200 K. Near the ordering temperature of the uranium moments a clear change in the domain wall motion is observed. The domain size analysis of the flower-like pattern reveals that the domain structure is consistent with a model of branching domains.