Cognitive linguists have been traditionally interested in uncovering the conceptual representation of cultural knowledge. For that endeavor, the semantic analysis of linguistic usage has become of prime importance in order to reveal metaphorical and associative schemas that as a whole are structured in so-called cultural models. Such models have been suggested for all sorts of events and institutions in the social world, among them also phenomena related to linguistic variation. However, it is less clear, first, how precisely cultural models arise in language contact situations and, second, how data-driven computational-semantic techniques can be employed for analyzing those models. As a case in point, we investigated the cultural conceptualization of regional Italian varieties. These varieties can be considered the result of recent contact between Standard Italian and one of the many local Italo-Romance dialects of Italy. The analysis of the cultural models draws on free association data gathered from 213 university students from all over Italy and further processed making use of Vector Space Models in order to extract semantic domains. Our results show that associations of semantic domains with varieties in contact situations differ across student groups and contact areas, so emphasizing the variability of cultural models. Furthermore, our quantitative approach has proven to be methodologically promising for capturing both expected and novel associative patterns in such very large datasets.