Is it necessary to remove old wasp nests

There are solar-powered gable fans - an Air Vent-brand fan can be picked up at Lowe's for just over $200:

The solar panel is on a cord, so it can be installed in the most sunny area while the fan sits in the gable.

From the Air Vent website:

The Gable-Mount Solar Vent is an exciting alternative to traditional attic ventilation. That's because it is powered by a solar panel that collects energy directly from the sun and converts it into electricity -- naturally -- to power a durable, high efficiency 24-volt DC motor. As a totally solar-powered solution, it's also environmentally friendly.

Painless Installation
The best installation feature is that the fan requires no electrical hook-up. That means no electrician and no complicated wiring is required, making the installation of your attic fan fast and easy.

It mounts in the gable end of the home, behind a decorative shutter (not provided, see below). The solar panel comes with brackets that allow for mounting on the roof.

Smooth Operation
The solar panel collects energy throughout the day under direct sunlight and converts it into "free" power to operate the fan -- providing ventilation during daylight hours, when it's needed most.

It creates up to 800 cubic feet of air movement per minute to remove uncomfortable heat in the summer and damaging moisture in the winter. And, the solar panel is wind-, hail- and impact-resistant to stand up to the elements.

Specifications

• Moves up to 800 cubic feet of air per minute
  
• Solar panel collects and delivers power under direct sunlight during the hottest part of the day without electrical cost
  
• Wind-, hail- and impact-resistant solar panel
  
• High efficiency, durable 24-volt DC motor
  
• 5-year limited warranty

_{(source: airvent.com)}

Model #SHT15W

• Plastic
  
• Sold in the color white only but it can be painted to match a home’s exterior
  
• Automatically opens when the power fan is running and then closes when the fan is not running
  

In case you haven't noticed, weather varies ;) This alone could account for the different effects each winter. But I think you're right, other factors are at play here.

Ventilation. Your gross vent area is 1/100 the attic area, accounting for louvers, let's say about 1/150th of attic area. If you do not consider the gable ends as cross ventilated, it is barely adequate. But as a cross ventilated arrangement, it is more than adequate. Will more help? Yes. Will it be effective? Harder to say. More on this later.

Moisture. Frost on nails alone is not necessarily cause for alarm. Black mold growing where the ventilation is less effective is definitely cause for concern. I'm no mold expert, but you should at least spray some moldicide on it while you devise a more permanent solution. Since the attic is always warmer than outside air, for there to be enough moisture to condense in the attic, the moisture had to come from either inside the house or from a roof or plumbing leak. Running a humidifier frequently would significantly contribute to the amount of moisture migrating into the attic. You don't mention anything about a vapor barrier, you quite likely do not know.The amount of moisture you observe tells me you don't have an effective moisture or vapor barrier. Not only can this cause mold, but it will also diminish the effectiveness of the insulation.

Why frost on only one side? Most likely solar access. The nails are colder on one side because the roof angles are different. This has significant effect on roof surface temperature, even under a good layer of snow.

Not only can vapor migrate through the ceiling, it can be carried in through air leaking around openings in the ceiling, in particular the pull down steps. If the perimeter is not weatherstripped, much moisture (and heat!) can escape this way.

What to do. Your primary focus should be to limit moisture migration into the attic. This will not only solve the condensation problem, but also limit heat loss. Seal all ceiling penetrations. Not only the steps, but plumbing and electrical penetrations as well. Apply an effective vapor barrier. This is not easy. You don't mention your ceiling finishes, this can make it easy or difficult or expensive. You could simply sandwich plastic between the current ceiling and a thin new ceiling finish. If you have an expensive existing finish, you may need to pull up the attic insulation and spray a barrier down on the back surface.

Note that if your household generates a lot of moisture, a good vapor barrier could cause you to have problems with condensation in your ceiling finish. The only solution to this is reduce moisture generation and increase whole house ventilation, ideally through a heat exchanger of some sort.

Once you've reduced the moisture migration, you may not have a mold problem in the attic any more. You may not need any more ventilation at all. The areas near the eaves obviously are not well ventilated, so the addition of soffit vents is the best approach if more is needed. You will need to drill many holes in the separation board to gain free communication with added vents.

If that works out to be too much effort, adding ventilation elsewhere can still benefit the lower areas, though not as well as soffit vents. Anything that increases ventilation will help. More static vents, power vents, ridge vents, turbine vents, they all have their own pros and cons, but they will all increase ventilation. You can do just one measure or a combination of measures. There is no right solution, but there is something that will make more sense than the other options.