THERE'S Sarah! And it's actually true that she probably should have brought a scarf, all absurdity aside.
The scarf thing is barely parody of the 1996 Tomb Raider, and much to my own personal shock, it's more than Lara did to cover up in the remake.
In the original, there's a cutscene in which Lara is wearing... SOMETHING over her standard outfit? It was like a hood with thin capes in the back and front with foolish aspirations of sort of being a cloak. It would possibly be better than nothing if there was no wind chill, but there was clearly strong wind blowing, so... Nonsense.
BUT, to be fair, they gave her SOMETHING, and it was a CGI cutscene in a 1996 video game that was the first of what would hopefully be a new franchise. Contextually, they did fine as far as I'm concerned.
In the remake, Lara's just in her default outfit. Give Nanase a tank top and backpack, and the scarf would put her ahead of Tomb Raider Anniversary Lara.