This survey article is concerned with the emergence of vision augmentation AI tools for enhancing the situational awareness of first responders (FRs) in rescue operations. More specifically, the article surveys three families of image restoration methods serving the purpose of vision augmentation under adverse weather conditions. These image restoration methods are: (a) deraining; (b) desnowing; (c) dehazing ones. The contribution of this article is a survey of the recent literature on these three problem families, focusing on the utilization of deep learning (DL) models and meeting the requirements of their application in rescue operations. A faceted taxonomy is introduced in past and recent literature including various DL architectures, loss functions and datasets. Although there are multiple surveys on recovering images degraded by natural phenomena, the literature lacks a comprehensive survey focused explicitly on assisting FRs. This paper aims to fill this gap by presenting existing methods in the literature, assessing their suitability for FR applications, and providing insights for future research directions.