Developing zero-shot human activity recognition (HAR) methods is a critical direction in smart home research -- considering its impact on making HAR systems work across smart homes having diverse sensing modalities, layouts, and activities of interest. The state-of-the-art solutions along this direction are based on generating natural language descriptions of the sensor data and feeding it via a carefully crafted prompt to the LLM to perform classification. Despite their performance guarantees, such ``prompt-the-LLM'' approaches carry several risks, including privacy invasion, reliance on an external service, and inconsistent predictions due to version changes, making a case for alternative zero-shot HAR methods that do not require prompting the LLMs. In this paper, we propose one such solution that models sensor data and activities using natural language, leveraging its embeddings to perform zero-shot classification and thereby bypassing the need to prompt the LLMs for activity predictions. The impact of our work lies in presenting a detailed case study on six datasets, highlighting how language modeling can bolster HAR systems in zero-shot recognition.