I know I'm coming in WAY late on the conversation, but there seem to be some misconception/misinterpretation going on.
Heaters only "dry out" the air if they are literally drawing humidified air out of the greenhouse. What we most commonly see, and misinterpret at "drying" is a reduction in the RH caused by heating. For example, let's say it is 1°C outside and raining heavily. The RH outside is 100% - the air is saturated, but that absolute mass of water is low. Bring that air inside and heat it up, and while the absolute mass of water in the air is the same, the capacity of the air to hold moisture goes way up, making the relative humidity - the percentage of its capacity - lower.
I also think the concern that a fogger will significantly drive up your heating bill is misplaced.
It takes a certain amount of energy to raise the temperature of a mass of water from A to B, and in this case "B" is a level that causes it to go into the air. That energy has to come from somewhere. Have a pond in the greenhouse, and energy is taken from the air, and put into the water. Have a fogger, and the exact same thing happens, although you've increased the surface area sufficiently to make it happen faster. You will see that energy consumption in your fuel or electric bill. Put a heater in that pond, and the energy is still going to be on your bill, isn't it?
However, if you have a nice, tight greenhouse, with very little leakage, the "spike" in energy consumption will only happen in the initial effort to boost the RH. Once it's in the air, all you're doing is maintaining the temperature, not paying to add more moisture to the air. And as was said, as you increase the humidity, the "cooling effect" of a fogger does down, so "refilling" the air from leaks and door opening shouldn't be significant.
So, that simply means that you need to "batten down all the hatches" to keep from losing the precious humidity and warmth, and you'll keep your costs at a minimum.
Nobody said this was a cheap hobby.