This paper develops a House Price-at-Risk framework to examine how housing subsidies, credit conditions, and supply factors influence the distribution of house price growth in Hungary. Using quantile regression with adaptive LASSO variable selection, we identify variables driving downside versus upside risks across multiple horizons. Financial stress dominates the lower tail at short horizons, while unemployment and affordability constraints become the primary drivers of downside risk at longer horizons. Housing subsidies exhibit pro-cyclical characteristics, concentrating significant positive effects on the upper quantiles while leaving the lower tail largely unaffected. Supply-side variables display horizon-dependent sign reversals, with construction permits exerting upward pressure on prices in the short run but moderating them as supply materialises. Uncertainty decomposition reveals persistent left-tail dominance across all horizons. These findings suggest that macroprudential frameworks should account for the distributional effects of housing subsidies, particularly their pro-cyclical influence on house price growth.