First of all, philosophers do care about the color of the sky. Or perhaps it would be appropriate to say that they care about what it means that something is colored, how color concepts function, what it would take for something to be colored, whether there are examples of colored things, and so on. For instance, some people would argue that there are no colors but phenomenal colors. Think of it as mental paint for simplicity's sake. They might say something like that color experience isn't veridical, that ascribing color properties to things involves ascribing to them properties that belong to subjective experience and cannot belong to the objective, that all color ascriptions are confused, and that there are no colored things. Others would agree that color experience doesn't quite get things right, but say that color talk is made true by dispositions of objects to cause certain experiences in us in systematic ways, and that therefore it is completely fine to say that things have colors. And some people would want to understand colors in terms of categorical properties, and some in terms of causal powers, and so on and so forth. But that's all quite besides the point.
Philosophers care about emotions too - always have. And they are probably going to keep caring. For one thing, emotions seem to be important for explaining how people act, and philosophers care about explaining how people act. They also care about the fact that emotions seem to give us reasons to do things. For instance, someone who loves somebody seems thereby to have reasons to do all sorts of things they wouldn't have reason to do if they disliked them, or if they didn't feel anything at all about them. And philosophers care about the nature of having reasons.
Emotions are also interesting because they seem important to morality. For one thing, we moralize emotions. Sometimes people say that (other) people ought to feel ashamed, and some emotions seem to call for moral approbation or disapprobation. If Ted were to happily hit his aunt in the face with a rock and never felt guilty in the least, most people would think his act worse than if he did so reluctantly and felt horrible afterwards. And then there's the fact that emotion is involved in moral judgment. This is really well established. Pretty much everyone who doesn't have a graduate degree in philosophy just goes with what "feels" right/wrong in a given situation when they moralize. And there are lots of issues raised by such findings which are of interest to philosophers.
And then there are questions about the nature of emotions and what theories of emotions are supposed to be like. Are emotions conceptually articulated? If so, what do they purport to represent? And how do they relate to moods and feelings? And to reason? And aren't there seemingly culturally specific emotions? Are emotions socially constructed or natural kinds or something else? And aren't emotions phenomena at the level of persons, rather than their cognitive components? How are you supposed to scientifically study things that seem to be so burdened by its role within a view of people as beigns who act for reasons rather than merely mechanistic things? Wouldn't it have to start by simply defining away the things that make emotions interesting? Can a psychological theory of emotion even begin to answer the philosophical questions? Cognitive psychologists are typically engaged in finding regularities and correlations, and to some extent in componential analysis to explain perceived capacities human beings have. And we still have no idea how to integrate cognitive and neuropsychology, so what are we to do with findings about which brain areas light up, anyway? There are lots of questions one might ask. Some of which are interesting, some of which may turn out not to be.
There are a lot of philosophers working on moral psychology, arguing interpretations of experiments with psychologists or trying to work out philosophical consequences of the psychological findings, and other such things. And there are philosophers working in the philosophy of psychology, studying the structure of psychological theories and theorizing, and philosophical problems that arise in the context of psychology. One such problem is how are we to integrate the different explanatory levels. We still don't have a very good idea of how personal/subpersonal cognitive/neurobiological/computational modes of explanation are supposed to fit together, or even if they are consistent. And then there are philosophers doing theoretical cog. sci. work. And so on and so forth.
I don't know if I've answered your question, but this will have to suffice for now.