In order to get the mini deer spell, you need to have someone cast a shape spell on you. This is the frog icon that shows up when your deer falls asleep in a fairy ring (mushroom circle). It may take a number of tries, as the same kind of spell will turn your deer into a number of different animals.
Pelts do save for mini deer, but they must go through a process to "retrieve" it every time they log in or reload their set. They cannot sneeze off pelts like a normal deer can, so in order to get their pelt back after another deer casts on them, they must either reload their set and go through the process again, or wait until the right pelt happens to get cast on them again. This is why most minis will complain if they are cast on.