Another vote for using a dehumifier in the basement in summer. And of course it's cooler down there because the ground below the surface is gradually cooler, approaching deep ground temperature with depth, somewhere near 50 F. The dehumidifier is needed for your health and the building's, because that basement temperature, in the low to mid 60s, is below the dew point of summer air much of the time. Cool that air to near its dew point and you've got near 100% relative humidity, and that's the reason it feels clammy. Condensation on/absorption by the walls and floor leads to that musty basement smell common to many homes, and to mold.
It's possible that the basement walls, if insulated at all behind the "finishing," weren't insulated properly, but have fiberglass batts up against the concrete. Here is a good read on how a basement should be insulated:
http://www.greenbuildingadvisor.com/...-basement-wall
Be careful about how you use that whole house humidification system (or did you mean DE-humification?). Adding moisture to interior air in winter can cause problems. In most cases, a house with excessively dry air in winter is a house that leaks far too much air. Such a house could stand a good blower-door-directed air sealing effort. Here are a couple of good reads on that issue:
https://www.energyvanguard.com/blog/...or-air-quality
https://www.energyvanguard.com/blog/...s-Infiltration