In recent years, the demand for the winter tourism market has increased, and competition among winter tourism destinations has intensified. The competitive advantage of destinations depends on the products. Although it is assumed that there is a linear relationship between product attributes and satisfaction, some studies show that this relationship may not be linear. This research aims to classify destination attributes according to the three-factor theory of customer satisfaction by examining linear and nonlinear effects of winter tourism destination attributes on overall customer satisfaction (OCS). The survey technique was used to collect data, and 551 questionnaires were collected from tourists. The linear relationship between destination attributes and OCS was examined by multivariate regression analysis, and the nonlinear relationship was analyzed by penalty-reward-contrast analysis. According to the linear assumption, tourism elements play a determinant role in OCS, whereas the nonlinear assumption suggests that protection–information and ski support elements are basic factors; tourism elements and skiing elements are performance factors; and price is classified as an excitement factor. The study shows that improving the attributes of products listed as basic factors prevents customer dissatisfaction and increasing the performance of the attributes classified within the excitement factor will positively affect the OCS.