The size dependence of electron-phonon coupling rate has been investigated by femtosecond transient absorption spectroscopy for gold nanoparticles (NPs) wrapped in a shell of sulfate with diameter varying from 1.7 to 9.2 nm. Broad-band spectroscopy gives an overview of the complex dynamics of nonequilibrium electrons and permits the choice of an appropriate probe wavelength for studying the electron-phonon coupling dynamics. Ultrafast experiments were performed in the weak perturbation regime (less than one photon in average per nanoparticle), which allows the direct extraction of the hot electron cooling rates in order to compare different NPs sizes under the same conditions. Spectroscopic data reveals a decrease of hot electron energy loss rates with metal/adsorbates nanosystem sizes. Electron-phonon coupling time constants obtained for 9.2 nm NPs are similar to gold bulk materials (a. 1 ps) whereas an increase of hot electron cooling time up to 1.9 ps is observed for sizes of 1.7 nm. This is rationalized by the domination of surface effects over size (bulk) effects. The slow hot electron cooling is attributed to the adsorbates-induced long-lived nonthermal regime, which significantly reduces the electron-phonon coupling strength (average rate of phonon emission).