Social media platforms have become primary arenas for climate communication, generating millions of images and posts that - if systematically analysed - can reveal which communication strategies mobilise public concern and which fall flat. We aim to facilitate such research by analysing how computer vision methods can be used for social media discourse analysis. This analysis includes application-based taxonomy design, model selection, prompt engineering, and validation. We benchmark six promptable vision-language models and 15 zero-shot CLIP-like models on two datasets from X (formerly Twitter) - a 1,038-image expert-annotated set and a larger corpus of over 1.2 million images, with 50,000 labels manually validated - spanning five annotation dimensions: animal content, climate change consequences, climate action, image setting, and image type. Among the models benchmarked, Gemini-3.1-flash-lite outperforms all others across all super-categories and both datasets, while the gap to open-weight models of moderate size remains relatively small. Beyond instance-level metrics, we advocate for distributional evaluation: VLM predictions can reliably recover population level trends even when per-image accuracy is moderate, making them a viable starting point for discourse analysis at scale. We find that chain-of-thought reasoning reduces rather than improves performance, and that annotation dimension specific prompt design improves performance. We release tweet IDs and labels along with our code at https://github.com/KathPra/Codebooks2VLMs.git.