If it is facts that are being dealt with, they seek to justify beliefs of fact by examination of evidence - the more evidence the better. Not content with merely gathering evidence to verify their opinions, they actively seek out evidence that would falsify it, and happily change their views in the light of such evidence. To some people 'moral reasoning' is an odd term. Morals are what you have, they are a matter for individual conscience, rather than a matter for reasoning like science or logic. Human beings, though, make decisions and many of these decisions are moral ones, involving judgements about the best thing to do.
Reasonable people seek reasons to direct and justify their decisions.
There are several strategies to choose from when reasoning about moral decisions. One is to be sensitive to the value system of one's social group, to be aware of the expectations others have, and the social contracts, overt or tacit that exist between kinsfolk, friends or wider social arrangements. Reasoners will not however, unquestioningly accept social expectations, but will measure them against some criterion of justification. Two criteria are commonly used. One is the consideration of the consequences of one's moral decision.