Large language models provide a promising framework for wearable-based health prediction by converting structured physiological and behavioral measurements into natural-language prompts. In this paper, we investigate whether pre-trained lightweight open-weight LLMs can predict depression and anxiety symptoms from short-horizon consumer wearable data. Using 4-8 days of Oura Ring data from 1,285 participants in the Northern Finland Birth Cohort 1986, we convert activity, sleep, heart rate, heart rate variability, demographic, and anthropometric measurements into structured prompts. We evaluate Llama 3.1, BioMistral, and Qwen 2.5 under zero-shot, rule-based, and few-shot in-context learning settings. To contextualize LLM performance, we compare them against machine learning models and recurrent neural networks. Our results show that prompt design is critical for LLM-based wearable inference. Zero-shot LLMs achieve high accuracy but largely predict the majority class, failing to identify participants with depression and anxiety symptoms. In contrast, few-shot prompting substantially improves positiveclass detection. Llama 3.1 with four in-context examples achieves the strongest performance, with 0.92 accuracy, 0.82 macro-F1, and 0.69 F1 for the positive class, among evaluated models. These findings suggest that lightweight LLMs can use in-context examples to better interpret structured wearable summaries and possibly provide a scalable direction for mental health prediction from consumer wearable data in combination with pre-trained LLMs.