Yes, dogs can see in color.

Dogs See the World in Living Color - D-brief | DiscoverMagazine.com
This study from the Russian Academy of Sciences should put to rest the old myth that dogs can only see in black and white. Scientists already knew this because dogs have two different kinds of cone receptors in their retinas which means they can differentiate between at least two wavelengths of light. Humans, of course, have three kinds of cones, so dogs are not as good as us at color vision, but we are well behind some other animals like the mantis shrimp for example which has up to 16 kinds of cones. So dogs essentially have about the same degree of color vision as a colorblind human. The term 'colorblind' is probably the reason why people misunderstand this condition. It does not mean the inability to see any color; it is just means an insensitivity to certain colors. In the case of dogs, they cannot see red or orange parts of the spectrum. They have no problem with green, blue, and yellow, however. The study described in the article above shows that dogs not only are capable of discerning color but actually use color cues when making decisions; even more so than other cues like brightness. The study design ingeniously simple: the dogs were trained to associate a reward with a cue that differed from non-reward cue in both color and brightness (dark yellow vs. light blue, or light yellow vs. dark blue). Then the cues were switched: if the dog had learned that dark yellow was the rewarded cue, for example, it was given the choice between light yellow and dark blue. If brightness were a more salient feature, the dog would look for a reward next to the dark blue cue even though it had associated a reward with dark yellow previously. However, 70% of the time, the dogs chose the cue that matched the color that they had seen before (i.e. if they had learned that dark yellow was associated with reward in the training trials, they chose light yellow in the test trials). Of course it is no surprise that dogs are not as good color vision as much as humans. Dogs rely on other senses such as scent much more than humans.