Heart Failure (HF) affects millions of Americans and leads to high readmission rates, posing significant healthcare challenges. While Social Determinants of Health (SDOH) such as socioeconomic status and housing stability play critical roles in health outcomes, they are often underrepresented in structured EHRs and hidden in unstructured clinical notes. This study leverages advanced large language models (LLMs) to extract SDOHs from clinical text and uses logistic regression to analyze their association with HF readmissions. By identifying key SDOHs (e.g. tobacco usage, limited transportation) linked to readmission risk, this work also offers actionable insights for reducing readmissions and improving patient care.