that most of us act differently on our "own turf". I think Darcy was basically comfortable in his surroundings, so his civility was natural, but he did have some reticence and discomfort at the end of his walk with Elizabeth at Pemberley Woods ("nor did he seem much more at ease: when he spoke, his accent had none of its usual sedateness; and he repeated his enquiries as to the time of her having left Longbourn, and of her stay in Derbyshire, so often, and in so hurried a way, as plainly spoke the distraction of his thoughts" and at "such a time much might have been said, and silence was very awkward. She wanted to talk, but there seemed an embargo on every subject.."). I think it is indeed realistic to suppose that his arrogance was somewhat of a disguise for a degree of social awkwardness and shyness.
(BTW, Matthew MacFadyen himself states in one of the P&P2 featured interviews that he views Darcy as shy)