They do run the night time shows through most of the year, depending on park hours.
The lights show on Hogwarts just changes things up depending on the season. For most of the year they have a "regular" show that typically runs several times a night, but at Halloween the last few years there has been a special "Dark Arts" version. Also I believe they have a different version during Christmas season.
The Cinematic Spectacular that is over on the USF side typically runs nightly as well.
The caveat is the park hours. If the park hours are on the shorter side (during a low season, or like now when Studios closes early for Halloween Horror Nights) they might not run because it's not dark enough. But during these low season periods if the parks close earlier, that's usually during the week but they'll have longer hours on weekend where they will run the night-time shows.
So for you in January, I'd wager you'd be able to see both (Hogwarts in IOA, Cinematic Spectacular in USF) as it gets dark early even if the parks are say only open to 7ish.