I've written most of this in pieces, and have to put it together into a cohesive fic now. I hope you like it. As you may notice, I have rather a weakness for Thorin being strong and commanding.
It all started innocently enough.
Poor Bilbo was sitting by the fire, wrapped in blankets, and shivering. A few of the dwarves offered condolences that he was so cold, but it hardly made a difference.
"I think Mr Baggins will freeze into a block of ice if he doesn't warm up soon – his clothes are hardly made for this climate," commented Thorin to the others, some of whom smiled. "Burglar!"
Bilbo looked round, used to being ordered about by Thorin.
The dwarf shifted a bit to make some space next to him. "Come and get warm under my cloak. A frozen burglar is of no use to anyone."
Bilbo scampered over to the offer of warmth, and when he was settled, Thorin pulled the cloak around them, took out his pipe and began to smoke. With the warmth, and the familiar smell of pipe smoke, and the soft chatter of the other dwarves, it is unsurprising that Bilbo fell asleep rather quickly. Thorin noticed, and tried to resist the smile that tugged at his lips as he noticed that the hobbit was sleeping peacefully and no longer shivering.
Bilbo did not expect to be invited to share Thorin's cloak again, so it came as a surprise when he was asked the next few nights, and more after that. (Well I say asked, more commanded.) It seemed that, as long as it remained cold, Thorin was willing to make room to keep the hobbit warm. Each night, Bilbo would wait to be called (he didn't want to impose or assume), usually simply by the word 'hobbit' or 'burglar', before he went over and was wrapped up in the warmth of the sky blue cloak.
The heat meant that Bilbo slept well, and each morning, Bilbo woke refreshed (apart from the occasional crick in his neck). The hobbit found it hard to tell whether Thorin was happier of a morning, now that they spent the night together (in the most innocent of ways possible, of course), or more grumpy. He never quite decided.
Balin watched Bilbo and Thorin every night; saw the gratitude and admiration that Bilbo didn't try to hide, and the grudging affection that Thorin did try, and managed to hide from all the others. But this kind of thing rarely slipped by Balin. He said nothing, though mused upon the cultural implications for Bilbo; while dwarves had no problem with two men in a relationship, hobbits thought it was queer and improper.
None of the other dwarves complained or thought it was strange; if Thorin was willing to keep their burglar from freezing to death without asking them to take turns, well they didn't mind – none of them wanted to share their cloaks, despite the hobbit's small size.