Most people with HD eventually exhibit jerky, random, uncontrollable movements called chorea, although some exhibit very slow movement and stiffness (bradykinesia, dystonia). These abnormal movements are initially exhibited as general lack of coordination and an unsteady gait and gradually increase as the disease progresses; this eventually causes problems with loss of facial expression (called "masks in movement") or exaggerated facial gestures, ability to sit or stand stably, speech, chewing and swallowing (which can lead to weight loss if diet and eating methods are not adjusted accordingly), and loss of determination. In the later stages of the disease, speaking is impaired with slurred words and uncontrollable movements of the mouth, eating and mobility are extremely difficult if not impossible, and full-time care is required.
http://en.wikipedia.org/wiki/Huntington's_disease Which explains why it might have seemed to Dylan that Woody Guthrie was oblivious to all of it
It does say there that Selective cognitive abilities are progressively impaired, whereas others remain intact. Abilities affected are; executive function (planning; cognitive flexibility, abstract thinking, rule acquisition, initiating appropriate actions, and inhibiting inappropriate actions), psychomotor function (slowing of thought processes to control muscles), speech like slurring of the words and some uncontrollable movement of the lips, perceptual and spatial skills of self and surrounding environment, selection of correct methods of remembering information (but not actual memory itself), and ability to learn new skills, depending on the affected parts of the brain., but I think he was not so much oblivious to everything as unable to show any reaction.
It's for the fic, actually :)