*Ōþilagaiʀ (Germanic) comes from Proto-West Germanic gaiʀ, from Proto-Germanic gaizaz, from Proto-Indo-European ǵʰoysós, from Proto-Indo-European ǵʰey- — winter.
Ancestry of “*Ōþilagaiʀ”, step by step
*Ōþilagaiʀ traces back through two separate lines of ancestry.