The objectives of the study were to estimate the repeatability of health and welfare traits and investigate their association with performance in three breeds of dairy goats reared under low-input farming systems in Greece. A total of 1210 goats of Eghoria (n = 418), Skopelos (n = 429), and Damascus (n = 363) breeds were assessed. Udder health, parasitic resistance, welfare, milk yield and quality, and body condition score were recorded monthly for two milking periods. Udder health records included somatic cell count (SCC) and total viable count (TVC). Based on combinations of SCC and TVC and thresholds set at >106 cells/mL and >2 × 104 cfu/mL, respectively, additional udder health phenotypes were defined. Parasitism included myiasis, tick infestation, gastrointestinal nematode (GIN) and cestode faecal egg count (FEC), and lungworm faecal larval count (FLC). Infection with each of the endoparasites was defined based on FEC/FLC. Welfare assessment parameters included the presence of ear and horn injuries, ocular and nasal discharge, body and udder abscesses, injury and lesions on the skin of different regions, diarrhoea, hernias, overgrown hooves, arthritis, lameness, and udder asymmetry. Trait repeatability and animal correlations were estimated. Significant (p < 0.05) repeatability was reported for all udder health and most welfare traits in all breeds, GIN and cestode FEC, and GIN and lungworm infection in Eghoria, and myiasis in Skopelos. Correlations of health and most of welfare traits with performance were non-significant or favourable. Overall, results demonstrate potential to improve health and welfare of the studied breeds without compromising performance.