Cold dark matter (DM) models for structure formation predict that DM subhalos are present in the Galaxy. In the standard paradigm of DM as weakly interacting massive particle, subhalos are expected to shine in gamma rays and to provide a signal detectable with current instruments, notably with the Large Area Telescope (LAT) aboard the Fermi~satellite. This is the main motivation behind searches for DM signals towards dwarf spheroidal galaxies and unidentified Fermi-LAT sources. A significant angular extension detected from unassociated sources located at relatively high latitudes is considered a smoking gun signature for identifying DM subhalos. In the present work, we systematically explore, by means of state-of-the-art models of cold DM halos in the Galaxy, the detectability of extended subhalos with Fermi-LAT. We simulate a DM signal exploring different assumptions of subhalos distribution in the Galaxy and DM profile, and reconstruct its flux through a realistic Fermi-LAT analysis pipeline. In the most optimistic case, we show that a detection of extended DM subhalos can be made for annihilation cross sections higher than $3 times 10^{-26}$ cm$^3$/s (for a 100 GeV DM mass), still compatible with existing gamma-ray constraints, and that, in this case, the preference for extension of the source (vs point-like hypothesis) is significant. For fainter signals, instead, halos not only do not show significant extension, but they are not even detectable significantly as point-like sources.
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