  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.
