Painting beards can be a very challenging effort when attempting to finish a wood carving. There are a ton of ways to accomplish the look that you want, but here is a process that I was shown a few years ago. The important thing when learning to do wood carving, is that not every way is best for everyone. You have to find what works for you and makes you proud of the result.
A local carver that I consulted when I first started trying wood carving showed me a trick that is basically antiquing, but is performed in layers. He does this process on his walking sticks and faces to add some age or wear look.
After carving the beard to the detail that you desire, give it a light coat of white or gray (depending on how dark you want it), to just begin to tint the beard. Next, using some polyurethane in a spray can, give it a very light dusting from about 10 to 12 inches away. Allow the dusting to dry slightly and then using either a spray stain or a slightly wet brush with a darker color, hit the entire beard and then immediately use a light cloth to wipe off the main surface of the beard, being careful not to hit the crevices too much.
When this is done, you should have a nice base color of the beard, with some darker highlights in the crevices. You can now leave it alone, or apply another very light round of the base color with a cotton ball in a dabbing motion to hit scattered areas without covering the entire beard again.