In this letter, we design and verify a novel nonlinear attitude controller for small fixed-wing unmanned aerial vehicles (UAVs) in the presence of dissipation. The attitude controller is designed using quaternions, which provide the physical insight for the control design by relating it to the geometry of rotations. We also show how the controller can be suitably modified to adaptively estimate quasi-static disturbances and compensate for aerodynamic damping by incorporating suitable refinements to the controller. The performance of the controller is then verified using simulations that demonstrate global stability against arbitrarily large initial attitude errors.