This study utilizes a large-scale language model (LLM) to conduct a post-hoc analysis of microtargeting strategies for climate change campaigns in meta (formerly Facebook) advertising. The study focuses on two key aspects: demographic targeting, such as gender and age, and fairness. We evaluate the accuracy of LLM's demographic targeting predictions and analyze strategies tailored to different target groups by providing rationales for each classification using the LLM-generated explanations. The analysis reveals that young adults are primarily targeted with messages emphasizing activism and environmental awareness, while women are engaged through topics related to caregiving and social movements. We also assess the bias of the model's predictions using fairness metrics such as demographic equity, equal opportunity, and predictive equity. While LLM's performance is generally strong, it exhibits bias, particularly in the classification of male targets. This study provides a useful framework that can contribute to improving the transparency, accountability, and inclusiveness of social media-based climate change campaigns.