The ToyBox Study investigated parental influences on preschool children’s healthy and unhealthy snacking in relation to child obesity in a large cross-sectional multinational sample. Parents and 3–5 year-old child dyads (n = 5185) in a kindergarten-based study provided extensive sociodemographic, dietary practice and food intake data. Parental feeding practices that were derived from questionnaires were examined for associations with child healthy and unhealthy snacking in adjusted multilevel models, including child estimated energy expenditure, parental education, and nutritional knowledge. Parental healthy and unhealthy snacking was respectively associated with their children’s snacking (both p < 0.0001). Making healthy snacks available to their children was specifically associated with greater child healthy snack intake (p < 0.0001). Conversely, practices that were related to unhealthy snacking, i.e., being permissive about unhealthy snacking and acceding to child demands for unhealthy snacks, were associated with greater consumption of unhealthy snacks by children, but also less intake of healthy snacks (all p < 0.0001). Parents having more education and greater nutritional knowledge of snack food recommendations had children who ate more healthy snacks (all p < 0.0001) and fewer unhealthy snacks (p = 0.002, p < 0.0001, respectively). In the adjusted models, child obesity was not related to healthy or unhealthy snack intake in these young children. The findings support interventions that address parental practices and distinguish between healthy and unhealthy snacking to influence young children’s dietary patterns.