To help mitigate climate change, power systems need to integrate renewable energy sources, such as solar, at a rapid pace. Widespread integration of solar energy into the power system requires major improvements in solar irradiance forecasting, in order to reduce the uncertainty associated with solar power output. While recent works have addressed short lead-time forecasting (minutes to hours ahead), week(s)-ahead and longer forecasts, coupled with uncertainty estimates, will be extremely important for storage applications in future power systems. In this work, we propose machine learning approaches for these longer lead-times as an important new application area in the energy domain. We demonstrate the potential of several deep sequence learning techniques for both point predictions and probabilistic predictions at these longer lead-times. We compare their performance for subseasonal forecasting (forecast lead-times of roughly two weeks) using the SURFRAD data set for 7 stations across the U.S. in 2018. The results are encouraging; the deep sequence learning methods outperform the current benchmark for machine learning-based probabilistic predictions (previously applied at short lead-times in this domain), along with relevant baselines.