Drawing textures is a consistent part of drawing anthropomorphic cartoons. Most of the characters will not have smooth skin like humans do. However, you don't want to waste time drawing every feather. You can use a number of cartoonists' techniques to indicate different textures.
Using a broken line and selective texture to draw a furry character
The simplest way to indicate fur is to draw the outline of the character's shape in a broken line. A few breaks in the line that sprout off as tufts of hair will give your character an overall hairy appearance. It's not necessary to overdo this — a few tufts will do the trick.
When drawing a texture that covers a large part of the body, such as scales on a fish or feathers on a bird, it is not necessary to actually cover the object with the texture. If you indicate a texture in some well-placed areas of the body, the reader will assume the texture spreads over the entire shape.
The best placement for selective texture is in areas that would normally fall into shadow. The exception to this rule is in dark-colored areas. In these cases, texture the areas that would get the most light.
Smooth textures are indicated in the way they reflect the light. The smoother the surface, the more pronounced the divisions between light and shadow will become. Conversely, pebbly or rough surfaces — such as rhinoceros skin — will create small nooks and crannies for the shadows to fall into.