Heritability studies represent an important tool to investigate the main sources of variability for complex diseases, whose etiology involves both genetics and environmental factors. In this paper, we aimed to estimate multiple sclerosis (MS) narrow-sense heritability (h2), on a liability scale, using extended families ascertained from affected probands sampled in the Sardinian province of Nuoro, Italy. We also investigated the sources of MS liability variability among shared environment effects, sex, and categorized year of birth (<1946, ≥1946). The latter can be considered a proxy for different early environmental exposures. To this aim, we implemented a Bayesian liability threshold model to obtain posterior distributions for the parameters of interest adjusting for ascertainment bias. Our analysis highlighted categorized year of birth as the main explanatory factor, explaining ~70% of MS liability variability (median value = 0.69, 95% CI: 0.64, 0.73), while h2 resulted near to 0% (median value = 0.03, 95% CI: 0.00, 0.09). By performing a year of birth-stratified analysis, we found a high h2 only in individuals born on/after 1946 (median value = 0.82, 95% CI: 0.68, 0.93), meaning that the genetic variability acquired a high explanatory role only when focusing on this subpopulation. Overall, the results obtained highlighted early environmental exposures, in the Sardinian population, as a meaningful factor involved in MS to be further investigated.