Large language models (LLMs) achieve strong performance in long-horizon decision-making tasks through multi-step interaction and reasoning at test time. While practitioners commonly believe a higher task success rate necessitates the use of a larger and stronger LLM model, multi-step interaction with a large LLM incurs prohibitive inference cost. To address this problem, we explore the use of low-precision quantized LLMs in the long-horizon decision-making process. Based on the observation of diverse sensitivities among interaction steps, we propose Dynamic Mixed-Precision Routing (DMR), a framework that adaptively selects between high-precision and low-precision LLMs at each decision step. The router is trained via a two-stage pipeline, consisting of KL-divergence-based supervised learning that identifies precision-sensitive steps, followed by Group-Relative Policy Optimization (GRPO) to further improve task success rates. Experiments on ALFWorld and WebShop demonstrate that our approach achieves a strong accuracy-cost trade-off over single-precision baselines.