Rusty is the horse who pulls a hansom cab. His only appearance is in "The Rye". Kramer takes over the cab while his neighbor is away in Disney World with his family after the neighbor offered to split the profits, which average $500 per day.
George asks Kramer to take Susan's parents out for a hansom cab ride on their anniversery. The point of this is to get them out of their building so that George and Jerry can sneak a marble rye bread from Schnitzer's into the apartment. Earlier, Frank Costanza had brought the rye to a dinner in the Ross's apartment, but took it back without them knowing because they didn't serve it.
Kramer feeds the horse Beef-o-Reeno because he bought 50 cans at a discount store and he wants to get rid of them. This causes the horse to become gassy and ends the cab ride prematurely. This ultimately leads to the Rosses discovering George's plan.