An airplane made that hole.
Not by just flying through it and swirling the visible cloud out of the way, that makes a different pattern which doesn't last nearly as long.
It turns out that in certain conditions, airplanes can actually induce rain or snow in a localized region of a cloud, and the precipitation is what clears the hole - the water droplets that make up the cloud fall because of the airplane.
The conditions required for this to work are actually very specific, and even depend on the type of airplane (propeller or jet).
First of all, the water droplets in the cloud have to be supercooled—below freezing, yet not frozen. This is actually more common than you might think; in order for cloud droplets to freeze, the water needs to be into the solid region of its phase diagram. For cloud droplets, they'll freeze even without a crystallization nucleus at about -40C. About 2-6% of clouds with the right temperature for airplane induced snow are supercooled instead of frozen; lower temperatures have a lower percentage of clouds that aren't frozen for reasons which should be fairly obvious.
An interesting thing about water is that the smaller the droplet, the lower the temperature has to be for them to freeze. One of the things I managed to retain from "bubbles" class was that the smaller the droplet and the tighter the curvature of the surface, the higher the pressure inside the droplet. Water has an oddball phase diagram because as pressure rises, the freezing point actually drops—for most chemicals, it's the opposite. When you introduce a crystallization nucleus into such a droplet, it triggers crystallization, sometimes simply by breaking the curvature of the drop's surface and releasing the pressure that was keeping it liquid.
So we have supercooled water droplets, and an airplane. One of the things airplanes do apart from fly and make lots of noise, is creating areas of lower pressure at certain parts of their anatomy while they're flying. Right above the wings, at the wingtips, at the jet engine intakes, and at the propeller tips are some of the common ones. When pressure drops, so does temperature. When I calculated this for the chinook wind this spring, it was adiabatic because all the air was doing the same thing so there was no temperature gradient; here, it's close to adiabatic because it happens so quickly there isn't enough time for much heat transfer.
According to the study, a jet plane at cruise can have up to 20C of temperature drop over its wings, and a prop plane can have 20 to 30C of temperature drop at its propeller tips. As I mentioned just above, water droplets of the size found in clouds will spontaneously freeze at -40C, even without a nucleation point. So, if the cloud has a high relative humidity and supercooled droplets at -20C, a jet plane can turn the droplets directly over its wings to ice.
These little ice particles, as soon as they leave the region of the jet's wing, stay frozen because the temperature is below freezing, and are nucleation sites for the supercooled water surrounding them. More droplets freeze to ice, and you start getting snow.
The researchers also did some simulations of atmospheric dynamics, setting up a cloud with the right properties, then introduced a line of ice droplets as you'd get with an airplane passing through. Their simulation matched satellite and radar observations of several different airplanes passing through several different clouds, and what happened in the hour and more after the plane was gone.
They also found, while doing the simulation, that the heat given off by the water freezing started some updrafts in the cloud which suspended the ice crystals, and matching downdrafts at the periphery of the ice area which evaporated the water droplets. This all happened after the airplane was gone, and according to known rules of ice crystal formation where water droplets evaporate and the water vapour condenses onto ice crystals to form snow. Taking away those heat effects in the model made it not produce the same hole they saw in their cloud observations.