Spiking Neural Networks (SNNs) claim to present many advantages in terms of biological plausibility and energy efficiency compared to standard Deep Neural Networks (DNNs). Recent works have shown that DNNs are vulnerable to adversarial attacks, i.e., small perturbations added to the input data can lead to targeted or random misclassifications. In this paper, we aim at investigating the key research question: 'Are SNNs secure?' Towards this, we perform a comparative study of the security vulnerabilities in SNNs and DNNs w.r.t. the adversarial noise. Afterwards, we propose a novel black-box attack methodology, i.e., without the knowledge of the internal structure of the SNN, which employs a greedy heuristic to automatically generate imperceptible and robust adversarial examples (i.e., attack images) for the given SNN. We perform an in-depth evaluation for a Spiking Deep Belief Network (SDBN) and a DNN having the same number of layers and neurons (to obtain a fair comparison), in order to study the efficiency of our methodology and to understand the differences between SNNs and DNNs w.r.t. the adversarial examples. Our work opens new avenues of research towards the robustness of the SNNs, considering their similarities to the human brain's functionality.