[Their mutual silence is perhaps more comfortable than one would assume, in both their conditions, or maybe it's exactly because of that, because of everything they've shared between each other before this that the silence is more easily understood by both than words would be. It lasts until the hospital, where they get swarmed by concerned nurses and doctors who force Bucky to lie down on a movable hospital bed so they can wheel him away. Bucky, though, delays it -- he doesn't quite let go, his hand finding Art's quickly and squeezing it lightly, a wordless gesture of his thanks and everything else he can't really convey... and then he's gone, for the next few hours at least as Art gets checked out by the doctors, as well.
... Bucky might have mumbled some insistent words about that as they were taking him away, not that they wouldn't have done it regardless.
After his wounds are treated, his arm set in a cast, Bucky gets a room to stay in until the next day -- and it's a room with two beds, the other one obviously there, empty and waiting, if Art ends up needing to stay overnight to treat his hypothermia. Whatever the case, as soon as Bucky wakes up, he looks around, for any sight of white-purple hair and that rumpled suit, before he even knows what he's doing, who he is looking for.]