Slicer saves a segmentation node in a 4D image, because all the segments are stored in one file. Other software expecting 3D images will not read it properly.
You can export the segments to labelmap nodes by right-clicking the segmentation in the Data module, and choose “Export visible segments to binary labelmap”. Then you can save these labelmaps in individual nrrd files. ITK-Snap can read these.
Just out of curiosity: why are you using ITK-Snap when you already use Segment Editor? My hunch is that everything you want to do can be done in Slicer. Please let us know.