The interstellar medium is known to be chemically complex. Organic molecules with up to 11 atoms have been detected in the interstellar medium, and are believed to be formed on the ices around dust grains. The ices can be released into the gas-phase either through thermal desorption, when a newly formed star heats the medium around it and completely evaporates the ices; or through non-thermal desorption mechanisms, such as photodesorption, when a single far-UV photon releases only a few molecules from the ices. The first mechanism dominates in hot cores, hot corinos and strongly UV-illuminated PDRs, while the second dominates in colder regions, such as low UV-field PDRs. This is the case of the Horsehead were dust temperatures are approximately eual to 20-30 K, and therefore offers a clean environment to investigate the role of photodesorption. We have carried out an unbiased spectral line survey at 3, 2 and 1mm with the IRAM-30m telescope in the Horsehead nebula, with an unprecedented combination of bandwidth, high spectral resolution and sensitivity. Two positions were observed: the warm PDR and a cold condensation shielded from the UV field (dense core), located just behind the PDR edge. We summarize our recently published results from this survey and present the first detection of the complex organic molecules HCOOH, CH2CO, CH3CHO and CH3CCH in a PDR. These species together with CH3CN present enhanced abundances in the PDR compared to the dense core. This suggests that photodesorption is an efficient mechanism to release complex molecules into the gas-phase in far-UV illuminated regions.