Does the geothermal activity influence the climate in Iceland?
Since micro climates of a location are mostly based on temperature and precipitation patterns, I would suggest that yes, if focusing on precipitation alone, one would expect rising heat from geothermal activity off the surface as a variable to affect the formation and release of precipitation. But one would have to check what part of the island geothermal activity was highest as the jetstream would drag weather west to east if nearby, and given that it is a small island, may not record such an occurrence as a significant effect from the rising heat available around Iceland. I did find this article which is somewhat supportable of a heat increase around Iceland due to geothermal activity > Douglass/Patel and Knox, 2005. GEOPHYSICAL RESEARCH LETTERS, VOL. 32 https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004GL021816