Heart failure (HF) is one of the leading causes of rehospitalization among older adults in the United States. Although clinical notes contain rich, detailed patient information and make up a large portion of electronic health records (EHRs), they remain underutilized for HF readmission risk analysis. Traditional computational models for HF readmission often rely on expert-crafted rules, medical thesauri, and ontologies to interpret clinical notes, which are typically written under time pressure and may contain misspellings, abbreviations, and domain-specific jargon. We present ClinNoteAgents, an LLM-based multi-agent framework that transforms free-text clinical notes into (1) structured representations of clinical and social risk factors for association analysis and (2) clinician-style abstractions for HF 30-day readmission prediction. We evaluate ClinNoteAgents on 3,544 notes from 2,065 patients (readmission rate=35.16%), demonstrating high extraction fidelity for clinical variables (conditional accuracy >= 90% for multiple vitals), key risk factor identification, and preservation of predictive signal despite 60 to 90% text reduction. By reducing reliance on structured fields and minimizing manual annotation and model training, ClinNoteAgents provides a scalable and interpretable approach to note-based HF readmission risk modeling in data-limited healthcare systems.