The interaction between dust, ice, and gas during the formation of stars produces complex organic molecules. While observations indicate that several species are formed on ice-covered dust grains and are released into the gas phase, the exact chemical interplay between solid and gas phases and their relative importance remain unclear. Our goal is to study the interplay in regions of low-mass star formation through ice- and gas-mapping and by directly measuring gas-to-ice ratios. This provides constraints on the routes that lead to the chemical complexity that is observed in both phases. We present observations of gas-phase methanol (CH$_3$OH) and carbon monoxide at 1.3 mm towards ten low-mass young protostars in the Serpens SVS4 cluster from the SubMillimeter Array and the Atacama Pathfinder EXperiment telescope. We used archival data from the Very Large Telescope to derive abundances of ice H$_2$O, CO, and CH$_3$OH towards the same region. Finally, we constructed gas-ice maps of SVS4 and directly measured CO and CH$_3$OH gas-to-ice ratios. The CH$_3$OH gas-to-ice ratio agrees with values that were previously reported for embedded Class 0/I low-mass protostars. The CO gas-maps trace an extended gaseous component that is not sensitive to the effect of freeze-out. We find that there is no straightforward correlation between CO and CH$_3$OH gas with their ice counterparts in the cluster. This is likely related to the complex morphology of SVS4: the Class 0 protostar SMM4 and its envelope lie in the vicinity, and the outflow associated with SMM4 intersects the cluster. This study serves as a pathfinder for future observations with ALMA and the James Webb Space Telescope that will provide high-sensitivity gas-ice maps of molecules more complex than methanol. Such comparative maps will be essential to constrain the chemical routes that regulate the chemical complexity in star-forming regions.
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