All the examples of plasma I have come across are visible. Is there any plasma which is not visible? For example, during a dark lightening we don't see the radiation because its gamma radiation. Is plasma formed during a dark lightening?
This from the ITER page
In the heart of the Korean tokamak KSTAR, in operation since 2008, a plasma pulse burns brightly. But don't be fooled—the brightest areas of the photo are in fact the coolest. At 150 million °C (the temperature in the centre), the plasma doesn't emit in the spectrum of visible light. © National Fusion Research Institute, Korea
So yes, plasma can be invisible .
Remember that plasma is a phenomenon of both high temperature and low pressure. Plasmas are ionized fluids, which occur either when the temperature is so high compared to atomic ionization energies, or when the fluid is so diffuse that charged particles are unlikely ever to find each other.
A common tool in ordinary vacuum systems is the cold cathode pressure gauge, which measures the pressure by measuring the conductivity of the residual gas. This sort of highly diffuse plasma is invisible.
Of course you knew that already: this is the type of plasma that makes up the interplanetary and interstellar medium, which is quite transparent.
Dark lighting is (evidently), the result of Bremsstrahlung radiaiton from fast moving free electrons in the air. It's not the usual re-attachment emission that I'm used to seeing in lab plasmas. But briefly, yes you could categorize this as a cold plasma (it's got a degree of net-neutral ionization).
There are also plasmas that might just not be visible to the naked eye. They're still emitting visible photons, but not in very large numbers. So any combination of small and weak could make that happen.
There are probably exceptions, but most thermal plasmas will produce visible light. The ionization that creates them takes a lot of energy. If that state is populated, you'll also have electrons bouncing around through all the other states in the associated atoms emitting various wavelengths in the process.