The humidistats absorb moisture from air according to how much moisture is available and the plastic sensor tapes expand and contract with temperature; this enables them to work with relative humidity. I think they are a marvel of engineering.
I question how the air in the attic could be 80F while the outdoor air is 30F; this might be the condition inside the insulated envelope, but not under a vented uninsulated roof. I am not so concerned about very cold temperatures, because then a humidistat on an exhaust fan would do what it is meant for, bring in colder outdoor air to absorb and drive out some of the moisture in the warmer attic air.
It is the milder temperatures approaching freezing that permits humidity to remain or even be drawn in with outdoor air, then to collect and freeze inside the attic. It is possible to draw in 90 percent Rh air at 55F into an attic that contains 80 percent Rh air at 45F with an attic humidistat; in this case it might be better not to have the fan humidistat. An outdoor humidistat controlling the fan with a setting for a dew point 20F cooler than the indoor fan humidistat setting would help. Dew forming on the cold membrane removes excess humidity from the cooler attic air at night, so the humidistat does not demand the fan; then in the warmer day, the collected dew does its soaking damage.
There is a balance between removing heat from the attic by added insulation and removing insulation to warm the attic membrane to prevent a lowered membrane dew point. An indoor humidistat alone may not be able to prevent moisture collection by an attic fan in some situations of the tropical/continental changeover climates of the Eastern shores.