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Displacements of the Earth's surface can be estimated using differential interferometric synthetic aperture radar. The estimates are derived from the phase difference between two radar acquisitions. When at least three such acquisitions are available, one can compute the displacement between the first and the third acquisition and compare it with the sum of the two intermediate displacements. These two are expected to be equal for a piston-like spatially uniform deformation. However, this is not necessarily the case in measured data. Such lack of phase closure can be due to decorrelation noise alone. It has also been attributed to complex scattering processes such as soil moisture changes or multiple scattering sources. However, the nature of these nonrandom effects is only poorly understood in cold regions, as the role of snow and freeze/thaw processes has not been studied to date. To distinguish the noise-like and the systematic effects, an asymptotic Wald significance test is proposed. It detects situations when the observed closure error cannot solely be explained by noise. Such situations with $p are observed at the Ku-band during snow metamorphism and melt and following a summer precipitation event in Sodankyla, Finland. They can also be prevalent (> 25%) in the X-band observations of ice-rich permafrost regions in the Lena Delta, Russia, indicating the presence of processes that can have systematic and deleterious impacts on the estimation of surface movements. Satellite-based monitoring of these displacements is thus possibly subject to complex error sources in high-latitude regions.