I have been able to see color in the Orion nebula (M42) with my 16 inch dobsonian from a heavily light polluted city. This is only in the center (trapezium area), where I can see a reddish color. Interestingly, it's much more difficult to see this red color from a dark location. Several other people in my astronomy club have also noticed this, and one explanation that I got was that the cone cells are still active in a light polluted city, so I'm able to notice the red color ( I don't know whether it's true). From a good dark location, I've seen color on many planetary nebulae such as the Ghost of Jupiter. You usually see these are greenish in color, if you have a suitably large scope. With my 16 inch, I've seen color in a small number of bright objects (almost always limited to greens), but most objects don't show color. Having observed in instruments ranging from 2 inch to 18 inches, it certainly seems like a larger aperture allows you to see color in a larger number of objects. In my personal experience, I've only been able to notice color in the brighter objects in scopes 16 inches and above.
Disclaimer: I don't have any mathematical relation for aperture v/s color visibility; it appears to depend heavily on the observers' eye.
There is no reason to see any red color in the Orion Nebula. Its brightest part is at the Trapezium, whose dominant star, Theta 1 C Orionis, has a reddened B-V color index of +0.20. That does not correspond to a red color in any sense of the sword!
But it is reasonable that it should sometimes be possible to see a green or blue-green color in planetary nebulas. The surface brightness of planetary nebulas is often high, and the emission from OIII at around 500 nm falls comfortably into the range of greatest color sensitivity in the human eye. Also, the OIII emission in planetary nebulas is often quite "pure", not mixed with yellow and red wavelenghts, which is always the case when it comes to light from hot blue-white stars.