Radiative cooling is a sustainable alternative to conventional vapor compression-based systems. However, achieving subfreezing temperatures remains a significant challenge particularly in humid environments where a strong atmospheric back-radiation and parasitic heat transfer often necessitate the use of vacuum chambers. Angular-selective thermal emission has been proposed as a strategy to mitigate radiative heat gain from the atmosphere. Nevertheless, a fundamental drawback of employing thermal emission selectivity, whether spectral or angular, is the accompanying reduction in the emitter’s total radiated power which diminishes the emitter’s ability to overcome environmental heating. In this work, we investigate the use of angular shields to introduce angularly selective thermal emission without reducing the emitter’s radiated power. We analyze the effects of spectral selectivity, humidity, and parasitic heating on the system’s net radiative flux and equilibrium temperature. Our analysis shows that spectrally selective thermal emission is necessary for efficient cooling. While engineered angular emission outperforms angular shields under high humidity, angular shields outperform in scenarios with parasitic heating, owing to their preservation of the emitter’s omnidirectional emission. Angular shielding can enable subfreezing temperatures with simple insulation when the average atmospheric transmittance exceeds 70%.