Horse iris recognition is a non-invasive identification method with great potential for precise management in intelligent horse farms. However, horses' natural vigilance often leads to stress and resistance when exposed to close-range infrared cameras. This behavior makes it challenging to capture clear iris images, thereby reducing recognition performance. This paper addresses the challenge of generating high-resolution iris images from existing low-resolution counterparts. To this end, we propose a novel hybrid-architecture image super-resolution (SR) network. Central to our approach is the design of Paired Asymmetric Transformer Block (PATB), which incorporates Contextual Query Generator (CQG) to efficiently capture contextual information and model global feature interactions. Furthermore, we introduce an Efficient Residual Dense Block (ERDB), specifically engineered to effectively extract finer-grained local features inherent in the image data. By integrating PATB and ERDB, our network achieves superior fusion of global contextual awareness and local detail information, thereby significantly enhancing the reconstruction quality of horse iris images. Experimental evaluations on our self-constructed dataset of horse irises demonstrate the effectiveness of the proposed method. In terms of standard image quality metrics, it achieves the PSNR of 30.5988 dB and SSIM of 0.8552. Moreover, in terms of identity-recognition performance, the method achieves Precision, Recall, and F1-Score of 81.48%, 74.38%, and 77.77%, respectively. This study provides a useful contribution to digital horse farm management and supports the ongoing development of smart animal husbandry.