He's bundling up for the mission. To use Tifa he's got to not have half-frozen limbs so he can move around a little.

Besides, there's no way in hell he'd stay home anyway. ...Not when he has to make sure Naoto's got a scarf and is toasty and stuff, too. Be a big stupid fretting mcfretbutt. The only topsicle Kanji will not accept is a Naoto Topsicle.