Nora has an interesting history, as she was one of the characters created originally for the Batman: The Animated Series. In what is largely one of the most critically acclaimed episodes of the entire run, "Heart of Ice," she was used to give Mr. Freeze a more relatable and humanizing backstory. In the show, she was terminally ill and cryogenically frozen by her husband while he searched for a cure. Her tube was apparently shut down by the CEO of the project, which drove Fries to become Freeze, seeking revenge. In his 40-year history before that, he had no ties to humanity, and Nora and his backstory were soon added to the comics (and subsequent adaptations).
Zap2It also got an official character description from Fox, giving a little insight into how the character will play on the series.
"Thanks to her smarts, sincerity and a lighthearted sensibility, she’s the only person who’s managed to connect with the otherwise emotionally cold cryogenicist. As her condition worsens and her husband becomes more desperate to save her life, Nora must make the ultimate choice: play the willing participant in Victor’s mad plan or sacrifice herself to stop the monster inside of him."
As that's written, it sounds like her story will certainly play out differently on this show than it has in the past, but with the same ultimate result. After all, this season of Gotham is subtitled "Rise of the Villains."