I don't think it's the case of just setting the white balance for "night mode". And even if it matters, switching just to arbitrarily chosen value won't help much - while, yeah, daylight WB varies between 5000-5600K, overcast sky and default white balance in most displays we use is at 6500K - so if you're "nightmoding", you'd have to go for values closer to 2000-2500K or even lower (warm, incandescent bulb or candlelight).
But there's an issue here - it may be tough to read text. It means you'll be actively working on deciphering words and you won't fall asleep so easily.
So to counter that, maybe brightness will be upped a bit and you'll effectively start mimicking daylight brightness (especially since it's not an ambient light, but targeted directly towards your face, at close distance)
Then, since it's often close distance, and it's basically reddish hue that's blasting at your retinas(even lowest brightness settings at night are really bright), it may result in cortisol pumping through your veins (cortisol level is at highest level when you wake up and slowly goes down during the day - the lower level, the "relaxed/sleepy" you should be; it should hit the lowest at midnight+-2 hours).
While blue light also lowers melatonin level (high level means "sleepy", low means "awake", in simplified terms), the heightened cortisol level resulting from reddish "night mode" may make going asleep harder.
Only solution is unfortunately going dark, preferably at least half an hour before getting to bed - or at least switching to warm ambient(not targeted directly at our eyes) light and grabbing a book.