Sentiment analysis in low resource, morphologically rich languages like Tamil remains a significant challenge due to limited annotated data, code-mixed usage, and orthographic variability in social media content. Addressing this gap is crucial for inclusive NLP research and regional language applications such as opinion mining and public sentiment tracking. The study evaluates the effectiveness of pretrained multilingual models in both zero-shot and supervised learning settings for sentiment analysis of Tamil tweets, focusing on the difficulty of dealing with an agglutinative, low-resource language for Tamil tweet sentiment classification. We assess encoder-only transformers (e.g., XLM-RoBERTa, DeBERTa-v3, MuRIL, IndicBERT, mBERT) and decoder-only LLMs (e.g., LLaMA 3.1, Gemma 3, Mixtral, Mistral) on two datasets: Tamil Tweet Binary Classification Dataset and a filtered binary subset of the ACTSEA dataset. In the zero-shot setting, XLM-RoBERTa-XNLI achieves an F1 score of 0.9697 on ACTSEA using natural language inference (NLI) prompting. Supervised fine-tuning of MuRIL yields an F1 score of 0.9101, while LaBSE embeddings combined with SVM reach 0.8914. Our findings highlight that NLI-finetuned encoder models and cross-lingual embeddings offer strong generalization in low-resource scenarios. This work emphasizes the importance of task framing, multilingual representation learning, and hybrid modeling strategies for effective sentiment analysis in underrepresented languages like Tamil.