Yes you can, you just have to find the body number for the deer. Code for a deer that will look like your current character Rudolph is:
Unit_Create=PLAYER,Unit,Body13,Head29,Mane32,Tail24,Wings4,PS_RudolphMat,Tuftless
(You enter this into the Preset.campaign file when you want to test your deer in game.)
I see you have 2 body images you are editing. You have to choose one you want to use. Body2Tex allows for non-uniform bodies, whereas BodyTex copies your characters left and right too look the same (like a butterfly's wings).
I recommend you looking at the other preset textures for a guide to how to colour the Tex files. Currently your eyes are in the wrong slots, the top slot is for eyelids, second slot is eyelashes (lines), third is for the 'whites' of the eye and last is the iris and pupil.
With your material file (PS_Rudolph) it seems you are on the right track, you just have to change all the words Character to your character name (Rudolph). Just search for the word Character in the document and replace all of them with Rudolph.