A wheelchair-bound Henry (at his max. age) goes back in time, accidentally gets shot by his father-in-law who's deer hunting; then returns to his proper time and dies before help can arrive. At the time he's shot, Henry appears to be standing in the woods but he might just be sitting in the snow. The father-in-law remarks that he doesn't see any tracks (indicating Henry didn't take any steps).
The incident of going to the hospital pre-dates getting shot and is re: treating for hypothermia in which use of his leg(s) is lost (in the book they're amputated; in the movie they saved CGI costs by just making one(?) crippled).