Yes, Robert Walton does mention “white nights” in one of his letters to his sister. Specifically, in the fourth letter Walton described the Arctic environment and its effects. He wrote:

“We are still surrounded by mountains of ice, still in imminent danger of being crushed in their conflict. The cold is excessive, and many of my unfortunate comrades have already found a grave amidst this scene of desolation. I mention them to you in order to celebrate their memory. The sun is forever visible; its broad disk just skirting the horizon and diffusing a perpetual splendour. There— for with your leave, my sister, I will put some trust in preceding navigators— there snow and frost are banished; and, sailing over a calm sea, we may be wafted to a land surpassing in wonders and in beauty every region hitherto discovered on the habitable globe. Its productions and features may be without example, as the phenomena of the heavenly bodies undoubtedly are in those undiscovered solitudes.”