Sansa has somewhat gotten used to surprise visitors of late and when she's told there's someone at the gates bidding entrance and wanting to see the Lady of Winterfell, she decides to go down there herself. She doesn't want a repeat of the situation with Arya and, considering she has no family left to make an appearance, she wonders who this might be. Jon wouldn't need to be granted entrance to his own castle so this must be someone begging favor - there's been a lot of those lately considering the bitter winds have blown and the snows have grown deep. Sansa tugs on her leather gloves and her fine fur cloak before heading down to the gates to inspect this visitor for herself.
Lord Baelish, of course, wants to come and see and Sansa doesn't stop him. When the visitor at the gates turns out to be the tallest, broadest man she's seen outside of the Mountain, she's pleased enough to let the ghost of a smile touch her lips before setting her face in the placid, blank expression she so often defaults to these days. The Hound. She hasn't seen him since the Battle of the Blackwater but he'd saved her that night and to hear Brienne and Arya tell it, he'd kept Arya alive and tried to get her back to Winterfell. That's enough for Sansa.
The sour look on Lord Baelish's face is enough for Sansa too and so she leads him inside, heedless of his road-stained clothes or his gruff manner. Sansa has handled quite a bit worse than The Hound in the years since she's seen him and she knows he's all bark and very little bite where she's concerned. "Come, then, I'll show you to some chambers and get you something to eat," she says, leading them through the bailey and into the castle proper. Part of her is pleased to show him her home, a girlish and stupid part of her, and she tamps that down; there's no place for frivolity any longer.
Once there's a bowl of stew set in front of him and he's settled in front of a fire in a snug set of rooms (with the doors firmly shut against interlopers, thank you), she tugs off her own gloves and cloak and gets a good look at him. He's as scarred as before, yes, but his is a welcome face. They need men like him for the war to come and Sansa is glad to take him into service, if that's what he wants.
"Ser Sandor, what has brought you so far North? The smarter thing to do would have been to go home to your own keep, I would think. You're a lord now."