Maintaining udder health and milk quality is important in dairy goat production; however, the interpretation of somatic cell count (SCC) in goats is complicated by physiological and non-infectious factors. This study evaluated the associations among udder and teat morphological traits, SCC, bacteriological status, and udder surface temperature in clinically healthy Saanen dairy goats. Udder conformation was assessed using a linear scoring system in multiparous goats (n = 70). Composite milk samples were collected at three lactation stages for SCC and milk quality analysis, whereas separate half-udder milk samples were used for bacteriological examination. Udder surface temperature was measured using infrared thermography (IRT) at the final sampling time point. Stepwise multiple regression analysis was applied to identify udder and teat traits associated with log-transformed SCC. The results showed considerable variation in udder conformation, with the greatest deviations observed for teat placement. Fore udder attachment, udder cleft, teat length, and teat form were significantly associated with SCC, with stronger attachment, a more distinct udder cleft, shorter teats, and a more cylindrical teat shape being associated with lower SCC. Bacteriological examination detected mastitis-associated bacteria in 45.0% of half-udder samples, mainly coagulase-negative Staphylococcus spp. and Corynebacterium spp., while the proportion of obligate udder pathogens was highest in the >2,000,000 cells/mL SCC category. Bacteriologically positive udder halves showed slightly higher surface temperatures than bacteriologically negative udder halves (p < 0.05), whereas no significant differences in udder surface temperature were observed among SCC categories. These findings suggest that udder morphology is associated with SCC and may be useful in phenotypic udder health assessment. IRT may provide complementary information on bacteriological status under standardized conditions, but its diagnostic value in dairy goats requires further validation in larger, longitudinal studies.