You may want to make a different size cookie than the normal 2-1/2 or 3 inch circle. No problem! Just take the paper snowflake and reduce or enlarge the size to fit the area you want to place the picture. Then move on to the tracing. This is great if you want to make a large cookie cake too!
If you use a recipe for a highly textured cookie, like gingerbread, oatmeal or chocolate chip, you can put a base layer of powdered sugar and water to create a very smooth area and then stencil your image on that. Actually, that can just add to how creative you can be with decorating cookies with stencils. For example, you can put a background of a red or green circle on top of the cookie behind a white snowflake. Make sure that the first layer of color has dried thoroughly before adding your image.
If you can’t find mylar or acetate at your local craft supply store, try transparency films at an office supply house. Just make sure that the material will accept pen or ink so that you can trace on it and that it will be safe to use with food items. Also, you have a large number of suppliers of stencil films on-line.