My son just got an Xbox One, and I want to play multiplayer games with him using the Xbox 360 in the same house on the same WiFi network. Are separate Xbox Live accounts needed to play multiplayer games on the same WiFi system? We are running the 360 version of COD.
You can't play cross platform with the exception of the Xbox One running select backwards compatible games that were downloaded. To that extent, it won't matter if you have separate accounts or not if the game isn't backwards compatible for the Xbox One.
But yes, you can share gold across multiple users as this states:
Multiple members of a household will be able to share a single account
The article also states:
"We want to make sure that you and your son both have your own account," Kilgore said, in describing the case of a father and son sharing an Xbox Live Gold membership. "We want you log in to get your stuff, and when he logs in to get his stuff. On that console, if you have Gold, he can use Gold as well."
That sounds just like your situation. The only thing is, certain games are only backwards compatible. See this list for all the current Xbox 360 games that Xbox One can also run and play with other Xbox 360s.