In-Context Learning (ICL) in Large Language Models (LLM) has emerged as the dominant technique for performing natural language tasks, as it does not require updating the model parameters with gradient-based methods. ICL promises to "adapt" the LLM to perform the present task at a competitive or state-of-the-art level at a fraction of the computational cost. ICL can be augmented by incorporating the reasoning process to arrive at the final label explicitly in the prompt, a technique called Chain-of-Thought (CoT) prompting. However, recent work has found that ICL relies mostly on the retrieval of task priors and less so on "learning" to perform tasks, especially for complex subjective domains like emotion and morality, where priors ossify posterior predictions. In this work, we examine whether "enabling" reasoning also creates the same behavior in LLMs, wherein the format of CoT retrieves reasoning priors that remain relatively unchanged despite the evidence in the prompt. We find that, surprisingly, CoT indeed suffers from the same posterior collapse as ICL for larger language models. Code is avalaible at https://github.com/gchochla/cot-priors.