Cut small animal shapes out of fabric or felt - simple ones, so that two sewn together can be stuffed with batting to create the critter. Decorate them as you like - simply, with a little embroidery, or by gluing tiny felt shapes onto them (e.g., black spots on a white cow), or with sequins, etc., and maybe a ribbon around the neck; - or more fancily, with beading, or ribbon embroidery, etc., etc. Hang from a ribbon loop sewn into the critter’s back. 

(You might, for example, make a set of crêche animals; or a set of a few pairs of animals to represent those in Noah’s ark; or a group of farm animals for a farmer or would-be farmer; or a bunch of different felines for a cat-lover; or your animals, if you have a menagerie.)