Biting Cold's appeal lies mainly in her ability to prevent opponents from reviving. Her SA2 counters all variants that revive themselves and/or their teammates, which is especially useful against Plot Twisted, Last Hope, and Kill Joy. Her SA2 no longer ignores on-death SAs like Immoral Fiber, so you're better off bringing a different fighter depending on the defender.
On Rift offense, her SA1 mainly serves as a safety net and is largely negligible if you don't make any mistakes. The regeneration she gains from her SA2 also helps her heal back up to a safe amount of HP, which allows her to get a higher HP bonus. As stated earlier, the main reason to use Biting on offense is to utilize her anti-revive. Her anti-revive makes fighting defenders like Plot Twisted, Last Hope, and Kill Joy significantly easier, as she only needs to defeat them once instead of the usual twice.
Biting's first main flaw is her stats. She shares the exact same stats with Firefly. While 10K attack at max level when Diamond isn't bad, it's not necessarily good either. As such, she'll need some considerable Atk % investment in order for her to wipe out her opponents on offense. Her second main flaw is the conditions under which her SA procs. Her SA1 only procs if she's near a corpse, and her SA2 only procs upon her defeating an opponent. Outside of those two circumstances, Biting Cold is effectively an SA-less Painwheel that must rely on her equipped BBs and SMs in order to deal with her opponent. Like any other Painwheel, she has no access to Precision, Immunity, Curse, or any moves that remove buffs, so she'll need support from other fighters like Surgeon General and Sketchy in order to take on certain defenders without struggling somewhat.
On Rift defense, Biting Cold can prove to be an annoying defender to take down. Since she is a Water variant, she is compatible with Frost Armor, one of the best Catalysts in the game. The ideal set-up for a defensive Biting would be Frost Armor + Don't Poke the Buer + Tainted Blood MA. This would force the attacker to bring an anti-buff variant (e.g. Stand Out, Silent Kill), run an Outtake to remove corpses from the stage, or manage corpses while attacking. An attacker that manages corpses poorly may find themselves struggling to take Biting down as she gains Barrier, Thorns, Armor, and reflects damage (either from Thorns, her MA, or from DPtB). Making mistakes against Biting can prove to be fatal. Losing a fighter to her will cause her to gain 5 stacks of Regen for 10 seconds. This forces the attacker to whittle her HP down again, or lose depending on whether or not the attacker's other fighters can win the fight. If the attacker manages to win, their time bonus may not be as high as desired.