Can’t you dissect the eyes and look for cones and just see if they contain chemicals that change under different color spectra?
In many cases it isn’t hard to tell. You can train them to respond to colors and test when they respond which way.
You can’t get at it this chemical way because it depends on how the animal uses the information. Humans have 4 different color channels in the chemical sense, but we only use 3 of them to create our sensation for color.
Just seeing how animals respond is pretty useless. That’s why for centuries they thought bulls saw red.
This Straight Dope column by Cecil Adams may be of interest: Are cats and dogs really color-blind? How do they know?
Thanks, that was the column that sparked the question. Trying thousands of tests seems like the wrong way to proceed.
Probably necessary to be sure, though. The anatomical observations that the animal is equipped with the hardware (which is also noted in the article), do not prove that it is actually functional. It could be the case that the cats had actually lost their color vision, and the cones and associated nerve responses were vestigial. In some sense, they might as well be, I suppose, given the amount of training it takes to get the cat to understand what you’re after. They clearly aren’t devoting a lot of cycles to noting what color anything is.
Indeed, a cats brain may not process colour - given that cats are nocturnal and that cones (colour detecting cells) are not very light-sensitive, it makes sense that more visual cortex processing is devoted to rods (black and white, movement and shape, not colour).
The other issue is that cat brains do not seem to link “happy” to “learning” in the way that dogs (and people) do - you can train a cat, but it is much harder to do than a dog - because a dog enjoys it and requires approval from the alpha. Cats - meh.
So while a cat can be trained to respond to colour - it’s brain probably isn’t set up for it, and (quite frankly), it just doesn’t care.
And I am a cat lover.
Si
the dive master has a laser pointer, and his male german shephard, will chase that red dot endlessly - as if he were a giant cat. he has no interest in the pointer - just the red dot.
he also sees the white light refractions from my make up mirror and will try to chase those. i’ve seen this great big dog stand up on his hind legs and fixate on the light, which is up on the ceiling!
Thats just contrast. To test colour discrimination, you need objects (buttons, food, whatever) that have the same contrast ratio but different colours. If the animal can make a determination between the two objects, they can discriminate colour.
For a cat - create a path of different colour panels (using same-contrast panels). Put the cat in the middle of the path. If the cat steps off the marked path, spray it with water. If you can get the cat in the middle of the path a second time without losing a limb, consider the experiment a success. 
Si (not an animal behavioral specialist)
The dog might not percieve the dot as red though, he might see it as light grey.
My dog seems to have difficulty seeing his red frisby against the green grass in twighlight conditions. He doesn’t seem to have the same problem with his blue frisby. Aside from colour, the frisbies are identical. This has led me to believe he may have some red/green colour blindness, though I cannot know of course.
I’ve been trying to look this up without success. What is the fourth color channel. Red green and blue are always mentioned, but no fourth.
And is also consistent with the results that dogs are deuteranopes, as reported at the end of Cecil’s article and elsewhere. Although, I have a nit to pick - “The researchers concluded that dogs suffer from a type of colorblindness that in humans is called deuteranopia.” … Since this describes a normal condition of canine vision, I might argue that they aren’t “suffering” from anything. You want a turtle observing that you “suffer” from trichromism?
High intelligence and teachability aren’t required. They determined that bees can see into the UV from watching them go to artificial (but nectar-containingh) “flowers” illuminated only with UV light. They sisn’t do it in the dark.
Since the Sixties our family has reminisced about, for one thing, our big fluffy black-and-white cat Archie and our solid black cocker-dachshund mix Duchess. Duchess was slightly bigger, but Archie always got first dibs on the food we served them.
One of the items we fed them was a cat-and-dog food “stew,” made of chopped beef, gravy, peas, and diced potatoes and carrots. We actually watched Archie do this: he would eat the beef and potatoes and carrots and lap up the gravy, and move the peas aside with one front paw–which I assume he couldn’t do if he couldn’t see colors. Well, he sure knew green from orange! 
From year to year at Christmastime, too, we’ve watched our cats investigate the ornaments on the tree, and I wonder if they’re just attracted by the ornaments glistening or whether the bright colors play a part in it, too. (After a couple of years Archie got so he couldn’t care less about the tree and other things those silly humans brought into the house.)
Or he could smell the difference, or feel it with his nose or tongue. I wouldn’t need my eyes to tell the difference between peas and carrot bits.
Or see that one is round, and one is cubed
I believe the fourth channel is the one we use to tell light from dark. The rods have varying sensitivity to different wavelengths just like the cones. And from the diagram in the wikipedia article on Colour Vision you can see that the “red”, “green” and “blue” receptors aren’t actually most sensitive to the colours we usually call “red”, “green” and “blue”.
Actually, “Green” and “Blue” respond pretty well to what we call “Green” and “Blue”. It’s only “Red” that’s off, because it responds to lower wavelengths as well. But it responmds further into the red than any other, so the use of the name “Red” is understandable.