As is usually the case with every new version of Halo, Halo 4 will require a substantial amount of space on your Xbox 360. Halo 4 will need at least 8GB of hard drive or flash memory card space to play the multiplayer modes, according to Xbox.com. The description on Xbox.com also notes that using the hard drive is "highly recommended" for those who want an "optimal" experience. I'm not sure who the people are that don't want an optimal experience when playing multiplayer mode... Here is what Xbox.com says specifically:
"At a minimum, you’ll need at least an 8GB USB Flash Drive or an Xbox 360 Hard Drive to play Multiplayer mode in Halo 4. For an optimal experience playing with an Xbox 360 Hard Drive is highly recommended. For Xbox 360 4GB, Arcade and Core consoles, the Xbox 360 Hard Drive is sold separately. See below for more details on the storage device options available for Xbox 360 and Halo 4."
This will probably be more of a concern to those who bought a 4GB Xbox 360 bundle than those who bought models with bigger hard drives. The page also offers some ideas on how to deal with a lack of hard drive space including a 16GB flash drive and the Xbox 360 320GB Media Hard Drive.
Halo 4 is schedule for release exclusively on Xbox 360 on November 6 of this year.