They were looking for a way to get out of the rain. That's what it really came down to. For once, the frantic search for a place to stay wasn't because they were trying to avoid the bite of a Wolfo's fangs or the paralysis of a Redead's screech. It wasn't because they were sneaking around the Gerudo Fortress (and on that note, a Hero he may be, but stealth was not Link's forte) or because one of Ganondorf's men had discovered them and decided that the King of Darkness would be most pleased with his find.
They'd been looking for a way out of the rain.
When the downpour had started, Link had looked at the sky- unconcerned as the droplets had drenched him. He'd scoffed and maybe hunched a bit closer to himself, but made no other sign that he even acknowledged the icy rain. It makes sense that after something like the Water Temple that the Hero of Time wouldn't be bothered by a little rain, but when getting wet was unnecessary, Sheik wasn't going to stand around in it. So he had insisted, and the Hero had agreed with a shrug of his shoulders and a sheepish grin.
And that's how they'd ended up in the Utility Shed at the very back of Lon Lon Ranch, a cow mooing loudly not five paces from them and straw mixing with Link's hair. It was warm and dry and blessedly quiet, away from all the screams and snarls that this world had dissolved into. Already Link is relaxing, the tension going out of his shoulders and the stiff line of his jaw. He shifts against the straw, scooting closer until Sheik feels the top of his head bump against his thigh. He doesn't see it, but he hears Link's jaw crack when an enormous yawn is loosed from the Hero's mouth. Within moments, his breathing has evened out.
Sheik looks at Link, the Hero of Time, asleep and faintly snoring against his thigh and for just a moment he is overwhelmingly grateful for this moment of peace, this sanctuary from the rest of their shriveled, dying world. Even if it does have the pungent and rather lingering scent of manure.