We report the results of low-temperature photoluminescence, room-temperature cathodoluminescence (CL) and scanning CL and electron microscopy of self-organized CdTe/ZnTe quantum dot (QD) structure. The in-depth profiling CL investigations were used to identify the microscopic origin of the CL emissions observed at 2.13,2.0-2.1 and 2.25 eV. In particular, we distinguish between CL emissions originating from the QD region of the structure and from the underlying buffer layers. Based on these measurements we assign the 2.13 eV CL band to the wetting layer and the 2.0-2.1 eV band to the QD emission. From the study of the in-plane and in-depth CL characteristics we demonstrate large in-plane fluctuations of the CL intensity and discuss their origin.