Despite mammography (MG) being among the most widespread techniques in breast cancer screening, tumour detection and classification remain challenging tasks due to the high morphological variability of the lesions. The extraction of radiomics features has proved to be a promising approach in MG. However, radiomics features can suffer from dependency on factors such as acquisition protocol, segmentation accuracy, feature extraction and engineering methods, which prevent the implementation of robust and clinically reliable radiomics workflow in MG. In this study, the variability and robustness of radiomics features is investigated as a function of lesion segmentation in MG images from a public database. A statistical analysis is carried out to assess feature variability and a radiomics robustness score is introduced based on the significance of the statistical tests performed. The obtained results indicate that variability is observable not only as a function of the abnormality type (calcification and masses), but also among feature categories (first-order and second-order), image view (craniocaudal and medial lateral oblique), and the type of lesions (benign and malignant). Furthermore, through the proposed approach, it is possible to identify those radiomics characteristics with a higher discriminative power between benign and malignant lesions and a lower dependency on segmentation, thus suggesting the most appropriate choice of robust features to be used as inputs to automated classification algorithms.