We use deep HI observations obtained as part of the extended GALEX Arecibo SDSS survey (xGASS) to study the cold gas properties of central galaxies across environments. We find that, below stellar masses of 10^10.2 Msun, central galaxies in groups have an average atomic hydrogen gas fraction ~0.3dex higher than those in isolation at the same stellar mass. At these stellar masses, group central galaxies are usually found in small groups of N=2 members. The higher HI content in these low mass group central galaxies is mirrored by their higher average star formation activity and molecular hydrogen content. At larger stellar masses, this difference disappears and central galaxies in groups have similar (or even smaller) gas reservoirs and star formation activity compared to those in isolation. We discuss possible scenarios able to explain our findings and suggest that the higher gas content in low mass group central galaxies is likely due to contributions from the cosmic web or HI-rich minor mergers, which also fuel their enhanced star formation activity. ; Comment: 20 pages, including two appendices; accepted to MNRAS