Climate warming may alter the quantity and timing of groundwater discharge to streams in high alpine watersheds due to changes in the timing of the duration of seasonal freezing in the subsurface and snowmelt recharge. It is imperative to understand the effects of seasonal freezing and recharge on groundwater discharge to streams in warming alpine watersheds as streamflow originating from these watersheds is a critical water resource for downstream users. This study evaluates how climate warming may alter groundwater discharge due to changes in seasonally frozen ground and snowmelt using a 2‐D coupled flow and heat transport model with freeze and thaw capabilities for variably saturated media. The model is applied to a representative snowmelt‐dominated watershed in the Rocky Mountains of central Colorado, USA, with snowmelt time series reconstructed from a 12 year data set of hydrometeorological records and satellite‐derived snow covered area. Model analyses indicate that the duration of seasonal freezing in the subsurface controls groundwater discharge to streams, while snowmelt timing controls groundwater discharge to hillslope faces. Climate warming causes changes to subsurface ice content and duration, rerouting groundwater flow paths but not altering the total magnitude of future groundwater discharge outside of the bounds of hydrologic parameter uncertainties. These findings suggest that frozen soil routines play an important role for predicting the future location of groundwater discharge in watersheds underlain by seasonally frozen ground.