LiDAR odometry is a fundamental component of autonomous robotic systems, relying on geometric registration between consecutive point clouds to estimate ego-motion. However, traditional geometric approaches often degrade in dynamic or unstructured environments due to unreliable correspondences caused by moving objects, sparse geometric features, vegetation, and semantically ambiguous structures. Existing works have shown that, some of these limitations can be addressed by introducing semantic information from the environment in the registration process. In this work, we build on this, and show that not all elements in the environment are equally relevant for registration. Hence, we propose a semantic class-weighted ICP for LiDAR odometry. Instead of strictly filtering out points belonging to specific semantic classes, the proposed approach weights the residuals of points belonging to semantic categories based on their expected geometric stability. This strategy enables informative but potentially unstable structures, to contribute to the registration process while mitigating the influence of dynamic objects. The experimental evaluation was conducted on the SemanticKITTI and RELLIS-3D datasets, which include urban, highway, rural, and off-road environments. The empirical results show that the proposed Semantic-weighted ICP improves pose estimation, especially in challenging off-road scenarios where conventional rigid features are scarce. Furthermore, the analysis reveals that the effectiveness of this weighting strategy is highly environment-dependent, influenced by the structural and semantic composition of the scene.