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Supercritical accretion onto compact objects may drive massive winds that are nearly spherical, optically thick, and Eddington limited. Blackbody emission from the photosphere is the direct observational signature of the wind. Here we investigate whether or not it can explain the soft emission component seen in the energy spectra of ultraluminous X-ray sources (ULXs). Based on high-quality XMM-Newton spectra of 15 ULXs, we find that the soft component can be modeled as blackbody emission with a nearly constant luminosity, and the 5 known pulsating ULXs (PULXs) in the sample display a blackbody luminosity among the lowest. These are consistent with the scenario that the soft emission originates from the photosphere of the optically thick wind. However, the derived blackbody luminosity for PULXs is significantly above the Eddington limit for neutron stars. A possible explanation is that a considerable fraction of the optically thick wind roots in the inner accretion flow, where the radiative flux could exceed the Eddington limit due to a reduced scattering cross-section or enhanced radiation transfer with magnetic buoyancy. Based on a wind model, the inferred mass accretion rate in these standard ULXs overlaps but is on average lower than that in luminous and very soft X-ray sources, which are also candidates with supercritical accretion. Alternatively, it cannot be ruled out that the soft emission component is a result of the hard component, e.g., via down-scattering in a cool medium, as a weak correlation may exist between them.