In this work, we report on local ferroelectric and piezoelectric properties of nanostructured polymer composites P(VDF-TrFE)+x(Ba,Pb)(Zr,Ti)O3 (x = 0 - 50 %). High-resolution imaging of ferroelectric domains, local polarization switching, and polarization relaxation dynamics were studied by piezoresponse force microscopy. In particular, we found that (Ba,Pb)(Zr,Ti)O3 inclusions usually show a strong unipolar piezoresponse signal, as compared to the polymer matrix. By scanning under high dc voltage the films can be polarized uniformly under both positive and negative electric fields. Stability of the polarized state is discussed.