Cortana isn't "really" nude, but she chooses to appear that way for a reason, according to 343 Industries.
Speaking with GamesRadar during a livestream, franchise director Frank O'Connor said the team at 343 added a backstory as to why AI construct Cortana appears to be nude in Halo games, as there was never a explanation provided in the lore.
Cortana was created using a flash cloned copy of Dr. Catherine Halsey's brain, and physically appears as a replica of Halsey when she was a younger woman. Due to the Cognitive Impression Modeling process her personality is decidedly human, unlike other AI, as Cortana retained Halsey's values, opinions etc.
Because of this, 343 wanted to add a reason for her choosing to appear in a form where only the naughty bits were covered, instead of just being something sexy to gaze upon.
"She's not really nude … but that's what it makes you think of," O'Connor explained. "So one of the reasons she [chooses to appear without clothes] is to attract and demand attention. And she does it to put people off so that they're on their guard when talking to her and she has the upper hand in those conversations.
"It's kind of almost like the opposite of that nightmare you have where you go to school in the nude," O'Connor said. "You're terrified and embarrassed and she's kind of projecting that back out to her audience and winning intellectual points as a result."
You can hear O'Connor explaining this around the 40 seconds mark in the GamesRadar+ How It's Done livestream.