Likewise, what are some subtle description the author gives to inform the reader of the sergeant-major's personality? How can we determine that one of the sergeant-major's defining characteristics is being an alcoholic?

The Sargeant-Major welcomes the offer of whiskey.

The sergeant-major shook hands, and taking the proffered seat by the fire, watched contentedly while his host got out whisky and tumblers and stood a small copper kettle on the fire.

The Sargeant-Major is more comfortable and outgoing after indulging in a few drinks. He's "bright-eyed".

At the third glass his eyes got brighter, and he began to talk, the little family circle regarding with eager interest this visitor from distant parts, as he squared his broad shoulders in the chair and spoke of strange scenes and doughty deeds; of wars and plagues and strange peoples.

He expects his glass to be refilled..... he doesn't ask for a refill, it is assumed that he needs one. 

The visitor absentmindedly put his empty glass to his lips and then set it down again. His host filled it for him.

From the Sargeant-Major's actions, it is simple to discern that he enjoys his liquor. Before having a few drinks, he is rather quiet and withdrawn. Afterward, he's enjoying himself. Also, his host doesn't hesitate to fill his glass, even after three or four drinks. Mr. White doesn't ask if he'd like anohter drink, he immediately knows to pour one.