Repeated transects have become the backbone of spatially distributed ice and snow thickness measurements crucial for understanding of ice mass balance. Here we detail the transects at the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) 2019-2020, which represent the first such measurements collected across an entire season. Compared with similar historical transects, the snow at MOSAiC was thin (mean depths of approximately 0.1-0.3 m), while the sea ice was relatively thick first-year ice (FYI) and second-year ice (SYI). SYI was of two distinct types: relatively thin level ice formed from surfaces with extensive melt pond cover, and relatively thick deformed ice. On level SYI, spatial signatures of refrozen melt ponds remained detectable in January. At the beginning of winter the thinnest ice also had the thinnest snow, with winter growth rates of thin ice (0.33 m month^-1 for FYI, 0.24 m month^-1 for previously ponded SYI) exceeding that of thick ice (0.2 m month^-1). By January, FYI already had a greater modal ice thickness (1.1 m) than previously ponded SYI (0.9 m). By February, modal thickness of all SYI and FYI became indistinguishable at about 1.4 m. The largest modal thicknesses were measured in May at 1.7 m. Transects included deformed ice, where largest volumes of snow accumulated by April. The remaining snow on level ice exhibited typical spatial heterogeneity in the form of snow dunes. Spatial correlation length scales for snow and sea ice ranged from 20 to 40 m or 60 to 90 m, depending on the sampling direction, which suggests that the known anisotropy of snow dunes also manifests in spatial patterns in sea ice thickness. The diverse snow and ice thickness data obtained from the MOSAiC transects represent an invaluable resource for model and remote sensing product development.