We present an abundance analysis of 96 horizontal branch (HB) stars in NGC 2808, a globular cluster exhibiting a complex multiple stellar population pattern. These stars are distributed in different portions of the HB and cover a wide range of temperature. By studying the chemical abundances of this sample, we explore the connection between HB morphology and the chemical enrichment history of multiple stellar populations. For stars lying on the red HB, we use GIRAFFE and UVES spectra to determine Na, Mg, Si, Ca, Sc, Ti, Cr, Mn, Fe, Ni, Zn, Y, Ba and Nd abundances. For colder, blue HB stars, we derive abundances for Na, primarily from GIRAFFE spectra. We were also able to measure direct non-local thermodynamic equilibrium He abundances for a subset of these blue HB stars with temperature higher than ~9000K. Our results show that: (i) HB stars in NGC 2808 show different content in Na depending on their position in the colour-magnitude diagram, with blue HB stars having higher Na than red HB stars; (ii) the red HB is not consistent with a uniform chemical abundance, with slightly warmer stars exhibiting a statistically significant higher Na content; and (iii) our subsample of blue HB stars with He abundances shows evidence of enhancement with respect to the predicted primordial He content by {Delta}Y=+0.09+/-0.01+/-0.05 (internal plus systematic uncertainty). Our results strongly support theoretical models that predict He enhancement among second-generation(s) stars in globular clusters and provide observational constraints on the second-parameter governing HB morphology.