It isn't so much he cares for her. He has apppearances to maintain.
It was after the first snow that it occured to him that the human brat looked cold. Her skin was pale and she shivered almost constantly. He didn't know why this surprised him. Now that he thought of it, his father's human concubine had always worn heavy clothing in the winter; wool and thick silks, with furs that his father hunted for, especially for her. He remembered how jealous the other females were, and he remember how she looked, trailing her heavy robes, bundled in warmth and his father's favor, and still shivering.
His memories aside, the brat was also human, and apparently needed better clothing for the winter. It was not that he cared for her, of course, but somehow she had become part of his retinue, and he could not allow her to be poorly dressed, or to become ill.
"I require," said Sesshomaru, "Clothing for a girl child. About this height." He held a hand at the brat's height and stared impatiently at the shopkeeper. "Warm clothing. The best you have."
The shopkeeper made an effort to speak, failed, and tried again. "Yes, my lord. At once, my lord. Er... it will take perhaps a week..."
"I require it now," said Sesshomaru. "This town stinks of humans. Your stench, in particular, offends me."
The shopkeeper gibbered. His mate, who had been watching from the back of the shop, slid next to him and hissed in his ear. The shopkeeper hissed back at her, apparently in some agony. Sesshomaru caught the words 'daimyo's daughter' and then 'kill us'. The human's mate hissed back 'all the same' and 'dog demon, you fool', and then 'rather risk the daimyo'. This conversation confirmed Sesshomaru's opinion of humans, which was that the females were weak, but the males were fools. Females were all weak, of course, even demon females, but human males left Sesshomaru wondering how his father's brat had managed to survive as long as he had, unfortunate incident (unfortunate that it failed to kill him, he meant) with a miko and a charmed arrow aside. He supposed it was the idiot's demon blood.
The hissed argument came to an end, and the female scurried off. The shopkeeper cleared his throat and pasted a sickly smile on his face. "As it happens, my lord," he said, "We just so happen to have a set of winter robes made for the daimyo's daughter. Perhaps my lord might find them acceptable...?"
Sesshomaru raised his eyebrow. The human turned gray. "Perhaps," he said. "But I doubt it."
The human female returned with her arms full of cloth. She shook out each piece carefully -- a complete set, as far as he could tell, of winter robes in thick silk and wool. Sesshomaru fingered the cloth -- acceptable, he supposed. "Adequate," he allowed. "Very well."
The shopkeeper bowed to the floor -- or slumped there in relief. "The honor is ours, great lord."
The female rolled the clothing carefully and offered it to him. He reached out to take it, and stopped. Humans often expected to be paid, didn't they? Personally he considered letting them live payment enough, but still, the brat often insisted that he pay for what food he bought for her. He even gave in sometimes, simply to silence her. He pulled a pearl out of his robes and handed it to the shopkeeper's mate.
The shopkeeper's eyes bulged out, and he stared at the pearl, greed written all over his face. Sesshomaru supressed an urge to rip his throat out. It would not do to have the brat's clothing bloodied. He did stare at him until the man went pale green and the stink of fear rose thick and arcid in the air. He smiled coldly at the shopkeeper's mate, and left.
"Thank you, Sesshomaru-sama!" The brat twirled and danced delightedly in her new robes. "They're so pretty! And so warm!"
"Hmph," he said.
"I don't know why my lord had to provide you with clothing," grumbled Jaken. "She's just a nuisance, my lord! Why can't we -- GCK."
Sesshomaru ground Jaken into the ground with his foot for a very satisfying moment. "Do you question me?"
"N-no, my lord!"
"Continue so," suggested Sesshomaru, and allowed him up.
He watched the brat admire herself in a frozen puddle, turning this way and that, and then smiling at him again. He stood up adruptly and stalked off.
"Where are you going, my lord?" wailed Jaken.
"Hunting," he snapped. "If anything happens to the brat, you die."
Rin would look well in fox furs.
And Merry Christmas, Tin! Thanks to everybody who put up with me whining did I get Fluffy-sama right.