We conducted a spectropolarimetric survey of 58 high proper-motion white dwarfs which achieved uncertainties of >~2kG in the H{alpha} line and >~5kG in the upper Balmer line series. The survey aimed at detecting low magnetic fields (<~100kG) and helped identify the new magnetic white dwarfs NLTT2219, with a longitudinal field B_l_=-97kG, and NLTT10480 (B_l_=-212kG). Furthermore, we report the possible identification of a very low-field white dwarf with B_l_=-4.6kG. The observations show that ~~5 per cent of white dwarfs harbour low fields (~10 to ~10^2^kG) and that increased survey sensitivity may help uncover several new magnetic white dwarfs with fields below ~1kG. A series of observations of the high-field white dwarf NLTT12758 revealed changes in polarity occurring within an hour possibly associated with an inclined, fast rotating dipole. Also, the relative strength of the {pi} and {sigma} components in NLTT12758 possibly revealed the effect of a field concentration ('spot'), or, most likely, the presence of a non-magnetic white dwarf companion. Similar observations of NLTT13015 also showed possible polarity variations, but without a clear indication of the time-scale. The survey data also proved useful in constraining the chemical composition, age and kinematics of a sample of cool white dwarfs as well as in constraining the incidence of double degenerates.