Sperm cryopreservation is effective in safeguarding genetic biodiversity in avian species. However, during this process, spermatozoa are very susceptible to plasma membrane peroxidation in the presence of high concentrations of reactive oxygen species (ROS). To mitigate this effect, the addition of exogenous antioxidants, such as hydroxytyrosol (3,4-dihydroxyphenylethanol; HT), an antioxidant derived from olive oil, to the cryopreservation sperm diluent, could be useful. To verify this, a cryopreservation diluent was supplemented with different concentrations (0 μg/mL, 50 μg/mL, 100 μg/mL, and 150 μg/mL) of HT. For this, semen was collected in 10 replicates from 16 roosters of the Utrerana avian breed, and a pool was prepared with the optimum quality ejaculates in each replicate. After cryopreservation, spermatozoa were thawed and different in vitro semen quality parameters were evaluated. A discriminant canonical analysis (DCA) was carried out and revealed that total motility (TM; Lambda = 0.301, F = 26,173), hypo-osmotic swelling test (HOST; Lambda = 0.338, F = 22,065), and amplitude of lateral head displacement (ALH, Lambda = 0.442; F = 14,180) were the variables with the highest discriminant power. Finally, a chi-squared automatic interaction detection (CHAID) decision tree (DT) was performed excluding fresh semen samples and ROS was found to be the most valuable variable to discriminate between the different established freezing groups. Samples in the absence of HT or with low concentrations of this antioxidant showed less desirable ROS values in cryopreserved rooster semen. The present study could lead to the improvement of cryopreservation techniques for the genetic material of local poultry breeds and optimize the conservation programs of endangered native avian breeds.