In order to edit the map sprite on the field map of a unit, you need to follow these steps--

1. Decompile Fire Emblem DS ROM.
2. Go to Data->3->Class Name
3. The "palette" file can be edited via a hex editor and contains the palette. Palettes are 0x200 bytes and are divided into two parts (not sure why there are 2 palettes or what each one does at the moment, haven't bothered to test). All the other files contain the graphical data for the different directions of movement.
4. By copying/pasting the files of one thing to another, you can literally switch the map sprites up.  Alternatively find a guide in this editor on LZ77-11 decompression and how to edit LZ77-11 compressed graphics so that you can actually alter the graphics.