Are there any extensions for SNAP to create training data for deep learning applications?
It depends on what you need. If it is labeled pixels with different classes over many scenes, I do not think SNAP can help (I can be wrong), but you could try with PixEx (Raster/Export/Extract Pixel values) to extract all information on bands (L1 or L2 products).
I guess you can also create containers with labeled polygons, like when you try to do a supervised classification, but this is done manually and it will take a long time.