We describe the growth of modulation-doped ZnSe/(Zn,Cd)Se quantum wells on (110) GaAs substrates. Unlike the well-known protocol for the epitaxy of ZnSe-based quantum structures on (001) GaAs, we find that the fabrication of quantum well structures on (110) GaAs requires significantly different growth conditions and sample architecture. We use magnetotransport measurements to confirm the formation of a two-dimensional electron gas in these samples, and then measure transverse electron spin relaxation times using time-resolved Faraday rotation. In contrast to expectations based upon known spin relaxation mechanisms, we find surprisingly little difference between the spin lifetimes in these (110)-oriented samples in comparison with (100)-oriented control samples.