The short answer is no...they see many colors.

The way that the eye works in higher mammals and most higher vertebrates ensures that most animals see and interpret some sort of color.

In animal eyes, there are two types of cells, rods and cones. The rods are very sensitive to light, but cannot detect color (basically they work as black and white, also known as "greyscale"). The cones detect particular ranges of color. We have three types of cone cells, which birds have five. This makes birds very sensitive to minor changes in color compared with humans.

Each nerve cell that sends signals from the rods and cones to the brain will be associated with 100-200 rod cells but only 1-5 cone cells. The effect of this is that animals have very sensitive greyscale vision that is low definition, or blurry. They tend to have very insensitive color vision, but the details in color are very sharp (high definition).

Evolution determines the balance of rods and cones in an animal's eye.

Animals that have adapted to living in the dark (nocturnal animals such as owls) tend to have far fewer cones, so that they only see in black and white. Animals which are active in the daytime (humans or hawks) have many cone cells and can see well in color.

You may notice that when you try to see in the dark you cannot focus well on things, but you "feel" like you can see things around you. In humans, the majority of rods (greyscale) are positioned around the outside of the eye, giving you good black/white peripheral vision. The majority of cones (color) are positioned at the center of the eye in an area called the fovea, so when you focus on things you see in color.

At night, your cones don't work very well, so you rely very heavily on your peripheral vision to navigate. The mental switch from cones to rods when the lights are suddenly turned off is what forces you to take time to "adjust" to the dark.

No, some animals see the full range of color as we do, and some see in black and white. Color vision has evolved several times independently over time. You can often guess if an animal uses color vision a lot by noticing if the animal itself is colorful.

In general, animals that are diurnal (active in the daytime) tend to have color vision, while animals that are nocturnal (active at night) tend to be "colorblind." There are millions of species of animals, though, so there are many exceptions to this rule.

It can be hard to measure color vision, because it's sometimes hard to know what an animal is seeing. Scientists used to think that finding out was as simple as looking for "cone cells" in the animal's eyes. These are the cells that can sense different colors in light. It's not that simple, though, because cats have very few cone cells, and they're normally nocturnal, but it seems that they can see the color blue better than scientists expected.

Some animals can see colors that we can't see. Bees, for example, can see in ultraviolet. Rattlesnakes can sense infrared radiation, but I'll leave it up to you whether or not to call that vision!

This is a really hard question to answer simply. Animals, from insects to fish to mammals, have a wide variety of vision types, and I can't make a good generalization about color vision.

Plus, nobody has gone out and tested every animal to find out how they see, so we just don't know about a lot of animals. However, I can tell you a few things about color vision that will help you figure out which animals can see multiple colors and which can't.

In vertebrates, there are two different types of photoreceptors in the eye: rods and cones. Rods are very good at seeing motion and seeing in low light, and cones are very good at resolving fine detail and seeing in color. A single cone can only see one color, so to be able to see all the colors that we see, an animal needs to have 3 different kinds of cones (red, green, and blue -- just like the 3 colors that TV sets use).

Birds have 4 kinds of cones, so they can see fantastic ranges of color that are hard for us to imagine. So ideally an animal would have lots of rods and lots of different kinds of cones and it could see everything very well. But it takes a lot of energy to make and maintain all those receptors and pigments, so an animal is limited in the number of receptors it can have. Also, there is a limited amount of space in the retina for these receptors to fit.

So an animal can have a lot of cones and see well in low light conditions, or it can have a lot of cones and see colors very well during the day, but it can't do both.

So nocturnal animals, like most mammals, including mice, cats, and dogs (I realize that your pet cat and dog aren't really nocturnal, but that's only because they've gotten used to hanging out during the day because that's when we feed them and give them attention -- wild cats and dogs are much more active at dusk and in the night than during the day) have lots of rods and see really well when there's not much light, but they don't have many cones. So they can't see color very well and also don't have very sharp vision.

Dogs can see some colors, but they only have 2 kinds of cones, not 3, so they can't see as many colors as us -- it's sort of like they're colorblind. Humans and most other primates are more diurnal (we're active during the day) and often need to be able to see different colors to survive. For example, fruit-eating monkeys have to use color to tell which fruits are ripe or nonpoisonous. So we have a lot of cones and few rods, and we don't see well at night. Birds are also usually active during the day and also need to be able to use color to identify foods, so they also have lots of cones and good color vision.

However, you can probably think of at least one well-known nocturnal bird that might have more rods than cones. Thinking about birds might also lead you to think of another way we can tell if animals can see colors. If you think about most of the birds you know, you'll notice that many of them have very colorful plumage. Often this colorful plumage seems to be used in mating -- females choose a male with the brightest colors. If it seems like animals are making decisions based on colors, then we know that those animals must be able to see colors. If an animal only needs to see one color (it just needs to know if something is red or not, for example), then it might just be able to see that one color. So we can now identify a lot of other animals that must be able to see multiple colors: colorful songbirds (they use colors to tell each other apart, to judge the quality of mates, and to find food), fish on coral reefs and in tropical streams (they use colors in ways similar to birds), and insects that pollinate flowers (they use colors to find the right flowers). Insects don't have eyes like we do, so they don't have rods and cones. Some of them can see colors, but not as many colors as we can. On the other hand, some honeybees can see 'colors' that we can't see, because they can actually see ultraviolet light. So some flowers that look white to us are quite colorful to honeybees.

I'm sorry this wasn't a simpler answer, but I hope it helped you understand how color vision works and why some animals do it better than others.