Interstellar dust grains are generally non-spherical and their major axes tend to orient perpendicularly to magnetic field lines. As a result, thermal emission from dust is polarized. This polarization provides information not just on dust itself, but also on the orientation of interstellar magnetic fields. The study of polarized dust emission -- which is found mainly at far-infrared and submillimeter wavelengths -- is central to many astrophysical fields, from the study of dust itself, to CMB analysis (as a foreground), and magnetic field mapping on both Galactic and molecular cloud scales. Unfortunately, interpreting the polarization fraction in emission (P/I) is a non-trivial task, since this quantity is determined by several degenerate factors: the orientation and structure of the magnetic field, the grain alignment efficiency and the optical properties of dust itself. One way of breaking this degeneracy is to study polarized emission at multiple wavelengths. As an example, if the same polarized structures are not visible at short and at long wavelengths, this likely means that cold dust in cloud cores is aligned and magnetic fields in cores are different from those in cloud envelopes. Also, if dust temperature is uniform, the effects of magnetic field structure on P/I are independent of wavelength and the spectral shape of dust polarization is mainly determined by dust properties. This would allow to trace the evolution of dust polarization cross-sections in the interstellar medium. I will show the preliminary results of a multi-wavelength polarimetric analysis in the star-forming region NGC 2071, conducted at three wavelengths: 850 micron (POL-2 observations from the BISTRO project at JCMT), 214 micron and 154 micron (HAWC+/SOFIA observations). The data show the potential for tracing variations of magnetic field orientation with optical depth, and/or grain growth in the higher-density region of the cloud, although more detailed modelling is needed to conclusively distinguish the two scenarios. I will further discuss which analysis techniques do not transfer well across wavelengths, and how including data at both short-wavelength (< 250 micron) and long-wavelength (~1 mm) was key to obtaining our results.