I've never been charged extra by Southwest for transporting my clubs. This webpage http://www.southwest.com/travel_center/sports_equipment.html seems to say there is no charge, though I think they could still charge you if the bag is outside the size (62" H+W+L) or weight (50lbs) limits.
They are transported as regular luggage, count against your three bag allowance and will be free IF they do not exceed 50#.
If these conditions are not met, then the appropriate charges will apply.
If they are close to or a little over the 50 pound limit, consider packing your shoes and balls in one of your other suitcases. That could certainly take well over five pounds off the golf bag.