You're certainly correct that there is a tendency in suppose that reason and emotion are antagonists, and that with respect to morality in particular, we should be guided by reason rather than emotion. And there may be major figures in the history of philosophy (Plato comes to mind) who really did see reason and emotion as in stark and irreconcilable tension. On this view, reason and emotion are essential partners in moral thought and deliberation instead of implacable antagonists.
However, there's a pretty significant segment of philosophers, both historical and contemporary, who don't think that reason and emotion are such enemies when it comes to moral reasoning and decision. A popular view (one that I myself find attractive) distinguishes between moral truth and moral knowledge: Emotions, on this view, are not a source of moral truth, but do enable you to know moral truths.
Suppose that, as you end a day of busy holiday shopping, you see a fellow shopper carrying a large bundle of shopping bags. She slips and falls on a patch of ice, evidently injuring herself. Feeling dismay, alarm, and sympathy -- what we might call morally salient emotions -- you offer help to the fallen shopper. Let us suppose that it is true that
It is morally right for you to help the fallen shopper.
In this case, your emotions helped you discern this truth. Without the ability to feel dismay, alarm, or sympathy, you would not have known that this is what it was morally right for you to do. However, it is not the case that it is morally right to you to help the fallen shopper because you felt dismay, alarm, or sympathy. It is morally right to help her because she needs aid, is in pain, it would be generous, and so forth. So on this view, your emotions help you to discern moral truths, but are not the source of that truth. Emotions are aids to moral reasoning, but are not what moral reasoning is about.
This position is attractive because it seems to reconcile two plausible claims. On the one hand, a person who lacks the right kind of emotional sensitivity is unlikely to appreciate what her moral obligations are and unlike to act reliably in morally praiseworthy ways. A person who (for instance) lacks all sympathy, respect, care, and so on, ends up morally deaf, cognitively cordoned off from moral realities. (At its worst, such a person exhibits psychopathy.) At the same time, emotions are imperfect signals of moral truth. Sometimes a person is sympathetic with, or cares for, someone who doesn't morally deserve sympathy or care. In other words, from a moral perspective, our emotional reactions need to be shaped or cultivated in the right way -- and the 'right way' is in accordance with reason.