Worldwide emission standards are now required to cover engine operation under extreme ambient conditions, which affect the raw emissions and the efficiency of the exhaust aftertreatment systems. These regulations also target new combustion technologies for decarbonization, such as neat hydrogen (H2) combustion or dual-fuel strategies, which involve a challenge to the analysis of exhaust aftertreatment systems requirements and performance. This work addresses the impact of high altitude and low ambient temperature conditions on the reactivity of an oxidation catalyst in the presence of H2. A reaction mechanism is proposed to cover the main conversion paths of CO, HC, and H2, including the formation and consumption of high-energy surface reaction intermediates. The mechanism has been implemented into a faster-than-real-time reduced-order model for multi-layer washcoat honeycomb catalytic converters. The model was utilized to investigate the effect of H2 concentration on the reactivity of CO and HC within the catalyst under various operating and ambient conditions. By applying the model and examining the selectivity towards different reaction pathways in the presence H2, insights into surface intermediates and reactivity across different cross-sections of the monolith were obtained. This analysis discusses the underlying causes of reactivity changes promoted by H2 and its relative importance as a function of driving boundary conditions.