Glacierized high-mountain basins supply water to approximately two billion people yet remain among the most data-scarce hydrologic regions globally, making truly ungauged streamflow prediction a critical challenge. Deep learning (DL) offers a promising alternative to traditional regionalization, but fundamental questions remain about when and why DL models generalize to a target domain that is not merely ungauged but hydro-climatically distinct from the training data. We address two questions: under what training data do DL models generalize reliably to completely ungauged glacierized basins? And how does model architecture, including physics-informed DL, modulate sensitivity to these conditions? We systematically evaluate three architectures — Long Short-Term Memory networks (LSTM), Graph Neural Networks (GNN), and differentiable HBV (δHBV) — across four experiments that control for training dataset size, hydroclimatic representativeness, and inclusion of basins with glaciers, using 2,845 basins from the Caravan global dataset with 283 target glacierized basins. We perform 100-trial repeated K-fold cross-validation by holding out glacierized basins as test basins strictly in space and time. Hydroclimatic representativeness of training data- the degree to which training basins cover the target glacierized regime consistently dominates both training data size and architecture choice as the primary determinant of generalization skill. Including glacierized catchments in training provides the strongest representativeness signal, with all three architectures achieving median NSE between 0.66 and 0.71. When glacierized catchments are excluded, LSTM median NSE falls to −1.43 in the most dissimilar partition; larger dataset size only partially improves skill (median NSE −0.96), confirming that dataset size cannot substitute for representativeness. Non-glacierized mountain catchments partially improve skill, demonstrating that partial hydroclimatic representativeness – through inclusion of non-glacierized mountain basins – contributes to model performance in glacierized basins. Architecture differences are secondary: δHBV and GNN show greater resilience under data scarcity due to structural constraints, but no architecture compensates for lack of hydroclimatic representativeness in training data. These findings reframe model selection for ungauged glacierized basins, highlighting the importance of representative training data and the potential limits of “out of sample in landscape” performance of DL models, specifically for DL deployment in climate impact assessments of high-mountain water towers.