Methods of producing anesthesia or analgesia at an ocular tissue site are provided. Aspects of the methods include contacting the ocular tissue site with a cooling element having a temperature ranging from 0 to −；30° C., such as 5 to −；20° C. for an application time of 30 seconds or less so as to produce anesthesia or analgesia at the target tissue site. Also provided are devices that find use in practicing the methods.
