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The solar wind interaction with planetary magnetospheres dictates the mechanism through which energy is transported across planetary systems. The magnetohydrodynamic plasma description suggests that solar wind conditions in the outer solar system encourage the magnetopause boundaries at Uranus and Neptune to be more Kelvin‐Helmholtz unstable, however, no quantitative assessment has been performed. To characterize the viscous solar wind interaction at Uranus and Neptune, we create an analytical model to determine where Kelvin‐Helmholtz Instabilities (KHIs) may form along their magnetopauses by searching for regions where the minimum condition for KHI formation is satisfied. We run the model at solstice and equinox for a range of Interplanetary Magnetic Field (IMF) strengths, and rotation phases. We find minimal seasonal variation for low IMF strengths (B = 0.01 nT), with ∼70% of the magnetopause surface at Uranus and ∼80% at Neptune, enabling KHI formation. For periods of stronger IMF strength (B > 0.3 nT), KHIs were significantly suppressed. While KHIs depend on both the conditions inside the magnetopause boundary and the shocked solar wind IMF strength, we find that the IMF strength is the most significant criterion in determining whether or not KHIs are allowed to form at the magnetopause boundaries. Plain Language Summary: As the solar wind travels through the solar system, it interacts with planetary magnetic fields. Understanding how the solar wind interacts with the magnetic fields is important because it dictates how mass, momentum and energy are transported through the planetary system. In the outer solar system, it is thought that vortex‐like structures called Kelvin‐Helmholtz Instabilities (KHIs) will form at the boundary where the solar wind reaches the planetary magnetic field. We present the results of an analytical model that determines where KHIs may form along this boundary. We find that, for both Uranus and Neptune, the KHIs are most likely to develop if the interplanetary magnetic field is small, at all rotation orientations, and at both their solstice and equinox magnetospheric configurations. Key Points: Kelvin‐Helmholtz Instabilities can form at the magnetopause at Uranus and Neptune at both solstice and equinoxKelvin‐Helmholtz Instabilities are more likely to develop in environments where the interplanetary magnetic field strength is smallBoth Uranus and Neptune see minimal variation in the regions where Kelvin‐Helmholtz Instabilities can form over a planetary rotation [ABSTRACT FROM AUTHOR]