  Aims. We aim to infer information about the magnetic field in the low solar
corona from coronal rain clumps using high-resolution spectropolarimetric
observations in the Ca ii 8542 A line obtained with the Swedish 1-m Solar
Telescope. Methods. The weak-field approximation (WFA) provides a simple tool
to obtain the line-of-sight component of the magnetic field from
spectropolarimetric observations. We adapted a method developed in a previous
paper in order to assess the different conditions that must be satisfied in
order to properly use the WFA for the data at hand. We also made use of
velocity measurements in order to estimate the plane-of-the-sky magnetic field
component, so that the magnetic field vector could be inferred. Results. We
have inferred the magnetic field vector from a data set totalling 100 spectral
scans in the Ca ii 8542 A line, containing an off-limb view of the lower
portion of catastrophically cooled coronal loops in an active region. Our
results, albeit limited by the cadence and signal-to-noise ratio of the data,
suggest that magnetic field strengths of hundreds of Gauss, even reaching up to
1000 G, are omnipresent at coronal heights below 9 Mm from the visible limb.
Our results are also compatible with the presence of larger magnetic field
values such as those reported by previous works. However, for large magnetic
fields, the Doppler width from coronal rain is not that much larger than the
Zeeman width, thwarting the application of the WFA. Furthermore, we have
determined the temperature, T , and microturbulent velocity, $\xi$, of coronal
rain clumps and off-limb spicules present in the same data set, and we have
found that the former ones have narrower T and $\xi$ distributions, their
average temperature is similar, and coronal rain has microturbulent velocities
smaller than those of spicules
