Woody was a member of the Earth Federation Forces stationed at Jaburo. He was engaged to Matilda Ajan and was going to marry her after the Battle of Odessa. Sadly, Matilda was killed during an attack by the Black Tri-Stars when Ortega's MS-09 Dom crushed her Medea transport.
Later in Jaburo, Woody assures Amuro Ray that it wasn't his fault Matilda died and that he should stop feeling so bad about what happened. Soon after, Zeon forces attacked the Federation base and Woody went out in a Fanfan hovercraft to attack them. Unfortunately, he ran right into Char Aznable and was soon killed in a similar manner as Matilda.
In Mobile Suit Gundam: The Origin, Woody's role is largely the same, but during the Battle of Jaburo, Amuro is nearly killed by Char's Z'Gok as he uses a GM while the Gundam is not available. Woody saves Amuro by attacking Char, and loses his life to the Zeon ace to allow Amuro to escape.
Woody also appears in the novelization in the same capacity. He's shown to be a bit jealous over a seeming attraction between Matilda and Amuro. Unlike the anime, Woody is presumed to have survived the One Year War.
Mobile Suit SD Gundam
Woody is one of the characters appearing in the OVA. He was seen along with Matilda, and he often speaks a line "I'm Woody".
Mobile Suit Gundam-san
Woody appears in the manga as "Woody-san".