Despite advances in deep learning, robustness under domain shift remains a major bottleneck in medical imaging settings. Findings on natural images suggest that deep neural models can show a strong textural bias when carrying out image classification tasks. In this thorough empirical study, we draw inspiration from findings on natural images and investigate ways in which addressing the textural bias phenomenon could bring up the robustness of deep segmentation models when applied to three-dimensional (3D) medical data. To achieve this, publicly available MRI scans from the Developing Human Connectome Project are used to study ways in which simulating textural noise can help train robust models in a complex semantic segmentation task. We contribute an extensive empirical investigation consisting of 176 experiments and illustrate how applying specific types of simulated textural noise prior to training can lead to texture invariant models, resulting in improved robustness when segmenting scans corrupted by previously unseen noise types and levels.