Context. "Snow lines", marking regions where abundant volatiles freeze out onto the surface of dust grains, play an important role for planet growth and bulk composition in protoplanetary disks. They can already be observed in the envelopes of the much younger, low-mass Class 0 protostars that are still in their early phase of heavy accretion. Aims. We aim at using the information on the sublimation regions of different kinds of ices to understand the chemistry of the envelope, its temperature and density structure, and the history of the accretion process. Methods. As part of the CALYPSO IRAM Large Program, we have obtained observations of C$^{18}$O, N$_2$H$^+$ and CH$_3$OH towards nearby Class 0 protostars with the IRAM Plateau de Bure interferometer at sub-arcsecond resolution. For four of these sources we have modeled the emission using a chemical code coupled with a radiative transfer module. Results. We observe an anti-correlation of C$^{18}$O and N$_2$H$^+$ in NGC 1333-IRAS4A, NGC 1333-IRAS4B, L1157, and L1448C, with N$_2$H$^+$ forming a ring around the centrally peaked C$^{18}$O emission due to N$_2$H$^+$ being chemically destroyed by CO. The emission regions of models and observations match for a CO binding energy of 1200 K, which is higher than the binding energy of pure CO ices ($\sim$855 K). Furthermore, we find very low CO abundances inside the snow lines in our sources, about an order of magnitude lower than the total CO abundance observed in the gas on large scales in molecular clouds before depletion sets in. Conclusions. The high CO binding energy may hint at CO being frozen out in a polar ice environment like amorphous water ice or in non-polar CO$_2$-rich ice. The low CO abundances are comparable to values found in protoplanetary disks, which may indicate an evolutionary scenario where these low values are already established in the protostellar phase. (Abbr. Version)