We study the low-temperature variation of the London penetration depth ${\ensuremath{\lambda}}_{L}(T)$ in superconductors having a mixed-symmetry order parameter. Two specific cases are considered: the $s+d$ and the $s+id$ symmetry, where the $d$-wave part of the order parameter is assumed to be of ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. We find as the key result that the low-temperature properties of ${\ensuremath{\lambda}}_{L}(T)$ can be used either to distinguish between a pure $d$-wave order parameter or a $(s+id)$-symmetric one having a small subdominant $s$-wave contribution in systems with a tetragonal lattice or to determine whether the order parameter of a superconductor with an orthorhombic lattice is $s+id$ symmetric or $s+d$ symmetric just by adding a moderate concentration of impurities.