Assessing horse welfare is a crucial issue for obvious ethical reasons but also because it has been shown to have an impact on reproductive and cognitive abilities. Welfare also affects the relationship of horses with humans both at work and outside work; it enhances security for people and thus it constitutes a social issue too. Studies combining behavioural, postural, physiological and sanitary data suggest that it is possible to identify and validate indicators of altered welfare but also of well-being, that is, of a positive affective state. Although it has been proposed that positive affective states could arise from the sum of positive emotions experienced daily, the link between these short term experiences and the chronic state that characterizes the welfare state is not clear yet. Indeed, emotions are short-lived affective reactions but do not necessary depict the chronic state of the animal. Moreover, identifying expressions of positive emotions remains more difficult than identifying those of negative emotions. Also discriminate valence (positive/negative) from intensity (high/low) when measuring emotions is both necessary and delicate. For example, adult play or anticipatory behaviours may not have the same valence if one considers the short term or the chronic affective state but are both of high intensity. On the other hand, other low intensity indicators of positive emotions emerge that might be better candidates for revealing a “well-being” state. The aim of this review is to propose a critical view of measuring short experienced positive emotions, evaluating their interest for welfare assessment and present novel perspectives of investigation through behavioural and electrophysiological recordings.