Recent advancements in large language models (LLMs) have led to their widespread adoption and large-scale deployment across various domains. However, their environmental impact, particularly during inference, has become a growing concern due to their substantial energy consumption and carbon footprint. Existing research has focused on inference computation alone, overlooking the analysis and optimization of carbon footprint in network-aided LLM service systems. To address this gap, we propose AOLO, a framework for analysis and optimization for low-carbon oriented wireless LLM services. AOLO introduces a comprehensive carbon footprint model that quantifies greenhouse gas emissions across the entire LLM service chain, including computational inference and wireless communication. Furthermore, we formulate an optimization problem aimed at minimizing the overall carbon footprint, which is solved through joint optimization of inference outputs and transmit power under quality-of-experience and system performance constraints. To achieve this joint optimization, we leverage the energy efficiency of spiking neural networks (SNNs) by adopting SNN as the actor network and propose a low-carbon-oriented optimization algorithm, i.e., SNN-based deep reinforcement learning (SDRL). Comprehensive simulations demonstrate that SDRL algorithm significantly reduces overall carbon footprint, achieving an 18.77% reduction compared to the benchmark soft actor-critic, highlighting its potential for enabling more sustainable LLM inference services.