The uplift of the Qinghai Tibet Plateau has led to a drastic change in the climate in Central Asia, from warm and rainy, to dry and less rainfall. Ammopiptanthus nanus, a rare evergreen broad-leaved shrub distributed in the temperate desert region of Central Asia, has survived the drastic climate change in Central Asia caused by the uplift of the Qinghai-Tibet Plateau. Ascorbate oxidase (AO) regulates the redox status of the apoplast by catalyzing the oxidation of ascorbate acid to dehydroascorbic acid, and plays a key role in the adaptation of plants to environmental changes. Analyzing the evolution, environmental response, and biological functions of the AO family of A. nanus is helpful for understanding how plant genome evolution responds to climate change in Central Asia. A total of 16 AOs were identified in A. nanus, all of which contained the ascorbate oxidase domain, most of which contained transmembrane domain, and many were predicted to be localized in the apoplast. Segmental duplication and tandem duplication are the main factors driving the gene amplification of the AO gene family in A. nanus. Gene expression analysis based on transcriptome data and fluorescence quantitative PCR, as well as enzyme activity measurements, showed that the expression levels of AO genes and total enzyme activity decreased under short-term osmotic stress and low-temperature stress, but the expression of some AO genes (AnAO5, AnAO13, and AnAO16) and total enzyme activity increased under 7 days of cold stress. AnAO5 and AnAO11 are targeted by miR4415. Further functional studies on AnAO5 showed that AnAO5 protein was localized in the apoplast. The expression of AnAO5 in yeast cells and the transient expression in tobacco enhanced the tolerance of yeast and tobacco to low-temperature stress, and the overexpression of AnAO5 enhanced the tolerance of Arabidopsis seedlings to cold stress. Our research provides important data for understanding the role of AOs in plant adaptation to environmental change.