Grandpa’s Packard is Grandpa Phil’s Car. It's a 1947 Packard Clipper in "Vermont Green Iridescent", with a tan interior. Despite being about fifty years old when the series takes place and lacking many modern features like air-conditioning, the Packard is Phil's daily driver and also serves as the "family car" for the entire boarding house. Phil even drives the car in bad weather, as seen in Snow when Arnold helps him mount the snow tires.
In addition to not having air-conditioning, the Packard also presumably lacks power steering and power brakes; The car also has an oil leak, as shown in Grandpa's Packard, but is shown to be ultimately reliable even though it's about fifty years old. Despite being old, lacking creature comforts and modern safety features, and presumably having high miles, the Packard is shown pulling a horse trailer with ease in The Racing Mule. It is entirely possible that Phil had the engine overhauled or replaced at some point. The Packard was damaged when Grandpa and Big Bob Pataki backed into each other on two separate occasions in Grudge Match, with damage being contrated to the right rear fender and trunk lid. Bob paid to repair the damage from the first fender bender after losing a golf game to Phil, though it is unknown who paid for the second round of damage. In Summer Love, Arnold, his Grandparents, and the four main boarders take the car to the beach on vacation. The Packard ends up in a large hole twice in Mr. Green Runs, though both times the damage is extremely minor.