I use this stitch for my fur and feathers. It is the perfect stitch for filling large areas but if you remember to follow the direction of the hair or fur growth with your stitches, you will see exactly why it is so good for realistic animal embroidery. It is also perfect for colour blending and shading.
If this is your first time using this stitch for fur or hair, I suggest two strands of thread.
Now, you can work in rows of alternating long and short satin stitch but I prefer to do small blocks. But you would start with a row of alternating long and short stitches. Remember to keep the upper edge of your stitches in a neat line or adjacent to the outline of your design e.g if you were embroidering one of my little hen patterns and started at the head, your upper line would curve with the top of the head.
Your second row would be sewing long even length stitches into the short stitches of your first row, putting your needle a little way into the tip of the stitch above it. Keep stitching those rows until your area is almost filled.
Your last row of stitches will fill the empty area but remember to finish the bottom of each stitch so that is on the line of your pattern outline
The best way that I can describe how I do this stitch for my animal embroideries, is that I approach it in a very similar way to painting, each stitch is like a very thin brushstroke.