Climate change in the Arctic is occurring at a rapid rate. In Longyearbyen, Svalbard, the world's northernmost city, deadly avalanches and permafrost thaw-induced architectural destruction has disrupted local governance norms and responsibilities. In the North Atlantic, the warming ocean temperatures have contributed to a rapid expansion of the mackerel stock which has spurred both geo-political tensions but also tensions at the science-policy interface of fish quota setting. These local climate-induced changes have created a domino-like chain reaction that intensifies through time as a warming Arctic penetrates deeper into responsibilities of governing institutions and science institutions. In face with the increasing uncertain futures of climate-induced changes, policy choices also increase revealing a type of "snowballing" of possible futures facing decision-makers. We introduce a portmanteau-inspired concept called "The Melting Snowball Effect" that encompasses the chain reaction ("domino effect") that increases the number of plausible scenarios ("snowball effect") with climate change (melting snow, ice and thawing permafrost). We demonstrate the use of "The Melting Snowball Effect" as a heuristic within a Responsible Research and Innovation (RRI) framework of anticipation, engagement and reflection. To do this, we developed plausible scenarios based on participatory stakeholder workshops and narratives from in-depth interviews for deliberative discussions among academics, citizens and policymakers, designed for informed decision-making in response to climate change complexities. We observe generational differences in discussing future climate scenarios, particularly that the mixed group where three generations were represented had the most diverse and thorough deliberations.