We study the effect of investment horizon on the optimal stock–bond–cash portfolio in a dynamic model with uncertainty about climate change. The stock risk premium is assumed to be an affine function of the average global temperature and an unobserved factor which is estimated via Bayesian learning. We assume that the probability distribution of future temperature is uncertain. The optimal investment strategy, robust to the uncertainty about climate change, is derived in closed form and analyzed for returns on the S&P500 index and the S&P500 ESG index. We find that stock market investment is quite sensitive to climate uncertainty with allocation to the S&P500 index being the most sensitive. We also show that, even for relatively short time horizons, welfare losses from climate uncertainty could be large for investments in either the S&P500 index or the S&P500 ESG index.