Our contribution focuses on a 3D numerical nonlinear analysis of galloping in a specific bundled overhead line with ice accretion. We studied the susceptibility to this self-excited oscillation, critical onset wind speeds, and global dynamic response of a very low-tensioned line with simulated icing observed on similar real conductors. Due to the highly nonlinear mechanical behavior of such a flexible cable, we employed the Newmark integration method combined with the iterative Newton-Raphson method. We analyzed two numerical models of the overhead line loaded by the wind: one assuming nonlinearity only in the wind load, while retaining the linearity of the mechanical system itself, and the other representing a fully nonlinear system including geometrical nonlinearity. Our analysis revealed that the determined critical wind speeds for the onset of galloping are in relatively close ranges for both models. However, numerical simulations with the fully nonlinear system indicated significantly lower amplitudes of limit cycle oscillations, especially at higher wind speeds, compared to the linear model of the line. This underscores the necessity of using fully nonlinear models during the design stage of such low-tensioned aerial conductors.