In this study, we examine the potential of leveraging self-supervised learning (SSL) and transfer learning methodologies for forest disturbance mapping using Earth Observation (EO) data. Our focus is on natural disturbances caused by windthrow and snowload damages. Particularly, we investigate the potential of knowledge distillation-based contrastive learning approaches to obtain comprehensive representations of forest structure changes using Copernicus Sentinel-1 and Sentinel-2 satellite imagery. Leveraging pre-trained backbone models from knowledge distillation, we employ transfer learning based on Deep Change Vector Analysis (DCVA) to delineate forest changes. We demonstrate developed approaches on two use-cases, namely mapping windthown forest using bi-temporal Sentinel-1 and Sentinel-2 images, and mapping forest areas damaged by excessive snowload using bi-temporal Sentinel-1 images. Developed self-supervised models were compared in a benchmarking exercise. The best results were provided by pixel-level contrastive learning for Sentinel-1 based snowload damage mapping with an overall accuracy of 84% and F1 score of 0.567, and for Sentinel-2 based forest windthrow mapping with an overall accuracy of 76.5% and F1 score of 0.692. We expect that developed methodologies can be useful for mapping also other types of forest disturbances using Copernicus Sentinel images or similar EO data. Our findings underscore the potential of SSL and transfer learning for enhancing forest disturbance detection using EO.