Medical image analysis frequently encounters data scarcity challenges. Transfer learning has been effective in addressing this issue while conserving computational resources. The recent advent of foundational models like the DINOv2, which uses the vision transformer architecture, has opened new opportunities in the field and gathered significant interest. However, DINOv2's performance on clinical data still needs to be verified. In this paper, we performed a glioma grading task using three clinical modalities of brain MRI data. We compared the performance of various pre-trained deep learning models, including those based on ImageNet and DINOv2, in a transfer learning context. Our focus was on understanding the impact of the freezing mechanism on performance. We also validated our findings on three other types of public datasets: chest radiography, fundus radiography, and dermoscopy. Our findings indicate that in our clinical dataset, DINOv2's performance was not as strong as ImageNet-based pre-trained models, whereas in public datasets, DINOv2 generally outperformed other models, especially when using the frozen mechanism. Similar performance was observed with various sizes of DINOv2 models across different tasks. In summary, DINOv2 is viable for medical image classification tasks, particularly with data resembling natural images. However, its effectiveness may vary with data that significantly differs from natural images such as MRI. In addition, employing smaller versions of the model can be adequate for medical task, offering resource-saving benefits. Our codes are available at https://github.com/GuanghuiFU/medical_DINOv2_eval.