The Natural Language to Visualization (NL2Vis) task aims to transform natural-language descriptions into visual representations for a grounded table, enabling users to gain insights from vast amounts of data. Recently, many deep learning-based approaches have been developed for NL2Vis. Despite the considerable efforts made by these approaches, challenges persist in visualizing data sourced from unseen databases or spanning multiple tables. Taking inspiration from the remarkable generation capabilities of Large Language Models (LLMs), this paper conducts an empirical study to evaluate their potential in generating visualizations, and explore the effectiveness of in-context learning prompts for enhancing this task. In particular, we first explore the ways of transforming structured tabular data into sequential text prompts, as to feed them into LLMs and analyze which table content contributes most to the NL2Vis. Our findings suggest that transforming structured tabular data into programs is effective, and it is essential to consider the table schema when formulating prompts. Furthermore, we evaluate two types of LLMs: finetuned models (e.g., T5-Small) and inference-only models (e.g., GPT-3.5), against state-of-the-art methods, using the NL2Vis benchmarks (i.e., nvBench). The experimental results reveal that LLMs outperform baselines, with inference-only models consistently exhibiting performance improvements, at times even surpassing fine-tuned models when provided with certain few-shot demonstrations through in-context learning. Finally, we analyze when the LLMs fail in NL2Vis, and propose to iteratively update the results using strategies such as chain-of-thought, role-playing, and code-interpreter. The experimental results confirm the efficacy of iterative updates and hold great potential for future study.