  Using magnetic force microscopy operating at sub-Kelvin temperatures we
characterize the heavy-fermion superconductor CeCoIn$_5$. We pinpoint the
absolute London penetration depth $\lambda(0) = 435 \pm 20$ nm and report its
temperature dependence, which is closely linked to the symmetry of the
superconducting gap. In addition, we directly measure the pinning force of
individual Abrikosov vortices and estimate the critical current density $j_c =
9 \times 10^4$ A/cm$^2$. In contrast to the related, well-established tunnel
diode oscillator technique, our method is capable of resolving inhomogeneities
$locally$ on the micrometer-scale at ultra-low temperature.
