At the dayside magnetopause, the magnetosphere often contains a cold ion population of ionospheric origin. This population is not always detectable by particle instruments due to its low energy, despite having an important contribution to the total ion density and therefore an impact on key plasma processes such as magnetic reconnection. The exact role and implications of this low-temperature population are still not well known and has not been addressed with numerical simulation before. We present 2-D fully kinetic simulations of asymmetric magnetic reconnection with and without a cold ion population on the magnetospheric side of the magnetopause, but sharing the same total density, temperature, and magnetic field profiles. The comparison of the simulations suggests that cold ions directly impact signatures recently suggested as a good marker of the X line region: the Larmor electric field. Our simulations reveal that this electric field, initially present all along the magnetospheric separatrix, is related to the bounce of magnetosheath ions at the magnetopause magnetic field reversal through Speiser-like orbits. Once reconnection widens the current sheet away from the X line, the bouncing stops and the electric field signature remains solely confined near the X line. When cold ions are present, however, their very low temperature enables them to E × B drift in the electric field structure. If their density is large enough compared to other ions, their contribution to the momentum equation is capable of maintaining the signature away from the X line. This effect must be taken into account when analyzing in situ spacecraft measurements.