Frank, up north, you need a humidifier in the winter and a dehumidifier in the summer.
Well, I got along fine without either for nearly all my life.
However, while I was using that antique hot-water vaporizer during the Deep Freeze, I noticed the cats tended to voluntarily gravitate towards that room, and that there seemed to be less scratching and fur shedding.
This had been of some concern to me, because remember, it got so unnaturally cold for such an unnaturally long time, and I was keep the cats indoors nearly all the time.
As for air-conditioners, this place has no air-conditioning. It can if one wishes, but the house is, really, rather large and leaks like a sieve excepting in winter, when all this temporarily "winterizing" stuff is up.
Since it's about 60% windows, during the summer, I simply open all the windows on all four sides, and position four floor fans to shove the air around. It's not nearly as good as air-conditioning, but obviously I survive.
I'm wondering if a dehumidifier would be of any good in such a setting, although it appears to me it would be good in only one room, perhaps. But if it wouldn't do any good for the cats, forget it.