Adapting text-to-image (T2I) latent diffusion models (LDMs) to video editing has shown strong visual fidelity and controllability, but challenges remain in maintaining causal relationships inherent to the video data generating process. Edits affecting causally dependent attributes often generate unrealistic or misleading outcomes if these relationships are ignored. In this work, we introduce a causally faithful framework for counterfactual video generation, formulated as an Out-of-Distribution (OOD) prediction problem. We embed prior causal knowledge by encoding the relationships specified in a causal graph into text prompts and guide the generation process by optimizing these prompts using a vision-language model (VLM)-based textual loss. This loss encourages the latent space of the LDMs to capture OOD variations in the form of counterfactuals, effectively steering generation toward causally meaningful alternatives. The proposed framework, dubbed CSVC, is agnostic to the underlying video editing system and does not require access to its internal mechanisms or fine-tuning. We evaluate our approach using standard video quality metrics and counterfactual-specific criteria, such as causal effectiveness and minimality. Experimental results show that CSVC generates causally faithful video counterfactuals within the LDM distribution via prompt-based causal steering, achieving state-of-the-art causal effectiveness without compromising temporal consistency or visual quality on real-world facial videos. Due to its compatibility with any black-box video editing system, our framework has significant potential to generate realistic 'what if' hypothetical video scenarios in diverse areas such as digital media and healthcare.