Primarily they are regarded as Time Lord art. It captures a piece of time, allowing it to be viewed for all eternity. Those within are trapped within a single moment. What isn’t clear is whether the subject of the painting is physical removed from the universe.
Taking a photo of someone does not trap them inside the image, but that is because it is only a copy of the original. When the Doctor says that it is a slice of real time does the painting contain that exact moment or just a duplication?
If it is the former then a stasis cube is an excellent way to remove a subject, either to protect it or to imprison it. It can also capture a whole landscape (whether it be a desert or a city) and everything within that area.
Since Arcadia didn’t vanish (and the Doctor doesn’t believe that it would have when he first sees the painting) we can presume that it is the latter. In which case there should be a copy of the War Doctor, in addition to the version that smuggles himself into Black Archive.
It is apparent that some crystal cubes can be used to transport people into a painting. The Zygons have taken images of landscapes and send soldiers inside. They are positioned some distance into the image in a different form that that which they went in.
It is possible that just as the painting transforms a slice of time so it appears to have been depicted with oil paint that it can be programmed to arrange those entering the picture into a specific form and place.
This could be the difference between taking a photo of an actual event and posing a shoot. ‘Gallifrey Falls’ is something that happened while the Zygon constructed pictures are artificial.
From the outside the events within the painting appear to be frozen. Yet we see that the three Doctors are able to take action, breaking out in much the same way that Zygons must have done.
The Zygon’s plan also hinged on them emerging when Earth was suitable for them. Therefore they must have had some awareness of the passage of time and possibly even a way to gather information about what was happening.
Since the War Council General says that they would be trapped in a single moment we could interpret that ‘moment’ as being a short period of time. A few minutes in which for the Doctors to engineer their escape.
It could be that the reason that it appears frozen from the outside is that time is passing incredibly slowly. Things are moving just at a rate that would be imperceptible to the casual observer.
There is also evidence that the moment preserved within loops forwards and backwards. When it is revealed that the Doctors are in the painting we see an exploding Dalek, as well as several other events, rewind.
The Dalek is knocked back a short distance before it crashes through the invisible barrier of the painting and it emerges in the Black Archive. It is important to note that not being able to see this would make it difficult to escape, but it is possible that placed subjects can be put near it.
It is clear that this barrier isn’t near the perspective of the actual painting. ‘Gallifrey Falls’ is high above the city, some distance from where the War Doctor stood and presumably the Zygon in the desert didn’t have to trek all the way across to reach the perspective of that painting.
It could be that the technology used to take the initial image for the painting captures a specific radius. The view point that can be set for any point within that radius but the barrier remains at the epicentre.
We can assume that ‘Gallifrey Falls’ isn’t a unique example of such Time Lord art. The Doctor is just surprised that this particular moment was captured and that it survived. Therefore there could be other paintings of different moments in history.
Time Lord PCs who consider themselves artists could produce similar paintings (or they might have in the past). The TARDIS would allow an artist to find a specific historic moment to capture and can be the main purpose of an adventure.
PCs could find other surviving pieces of art. If they could find a way to enter and leave using the crystal cubes the Zygons possessed they’d be able the past and other planets without a Time Lord or a time machine.
While they might have only a brief time inside it could be enough to explore without fear of disrupting history. This allows them to revisit places as often as they like, as each cycle gives them a chance to look at things from a new perspective.
Are the Zygons the first to consider putting people into a painting? Were their Time Lords who enjoyed creating fantasy pictures by inserting things from different time and places into a painting just for the resulting image?
The Zygons do appear to be the first to consider using a painting as a means of suspended animation. PCs might adopt this tactic, especially if they must travel the slow path. They can just hop in a prepared painting and have an ally bring them out at a later date, or they can break out themselves.
The PCs might also use this as a method of dealing with their enemies. It is recommended that living beings should only be transported if they are captured and can be forced to touch the crystal cube.
In this manner the PCs TARDIS will have both an art gallery and a prison, all in one.