Dust grains play an important role in the synthesis of molecules in the interstellar medium, from the simplest species to complex organic molecules. How some of these solid-state molecules are converted into gas-phase species is still a matter of debate. Our aim is to directly compare ice and gas abundances of methanol (CH$_3$OH) and CO, and to investigate the relationship between ice and gas in low-mass protostellar envelopes. We present Submillimeter Array and Atacama Pathfinder EXperiment observations of gas-phase CH$_3$OH and CO towards the multiple protostellar system IRAS05417+0907 located in the B35A cloud. We use archival AKARI ice data toward the same target to calculate CH$_3$OH and CO gas-to-ice ratios. The CO isotopologues emissions are extended, whereas the CH$_3$OH emission is compact and traces the giant outflow emanating from IRAS05417+0907. A discrepancy between submillimeter dust emission and H$_2$O ice column density is found for B35A$-$4 and B35A$-$5, similar to what has previously been reported. B35A$-$2 and B35A$-$3 are located where the submillimeter dust emission peaks and show H$_2$O column densities lower than for B35A$-$4. The difference between the submillimeter continuum emission and the infrared H$_2$O ice observations suggests that the distributions of dust and H$_2$O ice differ around the young stellar objects in this dense cloud. The reason for this may be that the sources are located in different environments resolved by the interferometric observations: B35A$-$2, B35A$-$3 and in particular B35A$-$5 are situated in a shocked region plausibly affected by sputtering and heating impacting the submillimeter dust emission pattern, while B35A$-$4 is situated in a more quiescent part of the cloud. Gas and ice maps are essential to connect small-scale variations in the ice composition with large-scale astrophysical phenomena probed by gas observations.
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