If you've built your biceps to a respectable size, your forearms should have some size of their own so your arms look balanced. Besides, strong biceps aren't much good unless the rest of your arm muscles -- forearms included -- are strong enough to assist and support them while lifting, pushing and pulling. You can feel the burn in your forearm muscles when you perform pullups, so you know they're getting some benefit from the exercise.
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When you do pullups you're targeting the latissimus muscles in your back, but there is a whole list of muscles that pitch in to assist your lats with the exercise. Your brachioradialis -- the forearm -- is on that list. Because you engage them when you do a pullup, they're a useful exercise to help build forearm muscles.
How often you should perform pullups depends on your goals. You shouldn't be doing them to get big forearms because they don't focus on your brachioradialis muscles. But if the goal is to work your lats, then twice a week -- every third day -- is an effective frequency. If your goal is to increase the number of pullups you can do, three times a week -- every other day -- is the regimen recommended by Brett Stewart in his 2011 book "7 Weeks to 50 Pull-Ups".
Just like the rest of your muscles, you need to allow your forearms to rest between workouts to maximize their potential for growth. However, since they are synergist muscles that assist with many arm movements, it's difficult to give them the rest they need between workouts for them to grow. Matt Siaperas, a personal trainer at Hardbodies Gym in Idaho, says that for forearm building, he would recommend that a client do exercises that focus on the forearm once a week and to get at least a 24-hour rest before doing exercises that will engage the forearms as assistor muscles, such as pullups. You could do this by either taking a day off from resistance training to do cardio, or do a leg workout the day after working your forearms.
Doing pullups two to three times a week, as well as performing other exercises such as cable pulldowns and upright rows, will work your forearm muscles a bit as assistor muscles. During the workout in which you focus on forearms, do curling exercises such as hammer curls, preacher curls, reverse curls and wrist rollers.