Sensei had claimed this coat was cold and heat resistant... They probably hadn't emphasized on the cold, though. The Stampede, in all his quickly-paced walk toward the lobby glory, was... freezing. His room had enough heaters to make it easily over ninety degrees, so the second he stepped into the normal (if a bit below) temperatured hallways, he... well. Froze. And as Plant, this was not a good thing; the cold had always, when he rarely experienced it (normally by townsfolk 'accidentally' locking him in the local meat freezer), made him want to do the equivalent of hibernation, or, in other words, sit in bed and sleep.
Buuuut, he couldn't do that. Because Akito had agreed to help him find the rabbits that they had to find fast, and Vash wasn't about to skip out on that. So concentrated on just moving correctly, the Stampede practically passed Akito, utterly distracted.
In fact, it wasn't until he'd actually crossed the lobby and gotten to the other door that he stopped, blinked, and back pedaled quickly, embarrassingly fidgeting and apologizing to Akito, who he - finally - noticed. "Ah, sorry! Really, really sorry..." Could a person sound more abashed? Not unless they were on sobbing, most likely.
And then... he took a moment to stare at the white thing in Akito's hands, brain working a bit slower than normal and not understanding what it was for a good five seconds.