This study was undertaken to investigate the diversity and population structure of 487 oat accessions, including breeding lines from the ongoing programs of the three largest Polish breeding companies, along with modern and historical Polish and foreign cultivars. The analysis was based on 7411 DArTseq-derived SNPs distributed among three sub-genomes (A, C, and D). The heterogeneity of the studied material was very low, as only cultivars and advanced breeding lines were examined. Principal component analysis (PCA), principal coordinate analysis (PCoA), and cluster and STRUCTURE analyses found congruent results, which show that most of the examined cultivars and materials from Polish breeding programs formed major gene pools, that only some accessions derived from Strzelce Plant Breeding, and that foreign cultivars were outside of the main group. During the 120 year oat breeding process, only 67 alleles from the old gene pool were lost and replaced by 67 new alleles. The obtained results indicate that no erosion of genetic diversity was observed within the Polish native oat gene pool. Moreover, current oat breeding programs have introduced 673 new alleles into the gene pool relative to historical cultivars. The analysis also showed that most of the changes in relation to historical cultivars occurred within the A sub-genome with emphasis on chromosome 6A. The targeted changes were the rarest in the C sub-genome. This study showed that Polish oat breeding based mainly on traditional breeding methods—although focused on improving traits typical to this crop, i.e., enhancing the grain yield and quality and improving adaptability—did not significantly narrow the oat gene pool and in fact produced cultivars that are not only competitive in the European market but are also reservoirs of new alleles that were not found in the analyzed foreign materials.