Students exhibit diverse cognitive styles, necessitating tailored educational approaches. However, the integration of Generative AI (GenAI) tools into design education presents challenges in accommodating the diverse cognitive styles of Industrial Design (ID) students. This study aims to identify students' cognitive styles in a GenAI environment, and examine how GenAI affects the design outcomes and processes of each cognitive style. We investigated the verbal protocols of 30 ID graduate students during conceptual design processes using Midjourney. To better distinguish cognitive styles, we segmented the protocols and encoded them into cognitive maps, ultimately identifying four primary cognitive styles: Associative Focusers, Focused Probers, Treasure Hunters, and Comprehensive Selectors. The cognitive maps also revealed that while GenAI notably enhances the frequency of reflections across all student groups, there are marginal significant differences between the cognitive styles. Additionally, two experts evaluated all design outcomes, finding no significant differences in novelty, diversity, integrity, and feasibility across different cognitive styles, indicating the balancing effect of GenAI on the design outcomes of students with different cognitive styles. These findings provide a theoretical foundation for further research on GenAI's impact on students, enhance understanding of GenAI's influence on design processes and outcomes, and offer insights for personalized ID education based on different cognitive.