Goats are essential to the dairy industry in Shaanxi, China, with udder traits playing a critical role in determining milk production and economic value for breeding programs. However, the direct measurement of these traits in dairy goats is challenging and resource-intensive. This study leveraged genotyping imputation to explore the genetic parameters and architecture of udder traits and assess the efficiency of genomic prediction methods. Using data from 635 Saanen dairy goats, genotyped for over 14,717,075 SNP markers and phenotyped for three udder traits, heritability was 0.16 for udder width, 0.32 for udder depth, and 0.13 for teat spacing, with genetic correlations of 0.79, 0.70, and 0.45 observed among the traits. Genome-wide association studies (GWAS) revealed four candidate genes with selection signatures linked to udder traits. Predictive models, including GBLUP, kernel ridge regression (KRR), and Adaboost.RT, were evaluated for genomic estimated breeding value (GEBV) prediction. Machine learning models (KRR and Adaboost.RT) outperformed GBLUP by 20% and 11% in predictive accuracy, showing superior stability and reliability. These results underscore the potential of machine learning approaches to enhance genomic prediction accuracy in dairy goats, providing valuable insights that could contribute to improvements in animal health, productivity, and economic outcomes within the dairy goat industry.