Predictive maintenance of railway infrastructure, especially railroads, is essential to ensure safety. However, accurate prediction of crack evolution represents a major challenge due to the complex interactions between intrinsic and external factors, as well as measurement uncertainties. Effective modeling requires a multidimensional approach and a comprehensive understanding of these dynamics and uncertainties. Motivated by an industrial use case based on collected real data containing measured crack lengths, this paper introduces a robust Bayesian multi-horizon approach for predicting the temporal evolution of crack lengths on rails. This model captures the intricate interplay between various factors influencing crack growth. Additionally, the Bayesian approach quantifies both epistemic and aleatoric uncertainties, providing a confidence interval around predictions. To enhance the model's reliability for railroad maintenance, specific constraints are incorporated. These constraints limit non-physical crack propagation behavior and prioritize safety. The findings reveal a trade-off between prediction accuracy and constraint compliance, highlighting the nuanced decision-making process in model training. This study offers insights into advanced predictive modeling for dynamic temporal forecasting, particularly in railway maintenance, with potential applications in other domains.