We present magnetization measurements on \ensuremath{\sim}3-nm $({\mathrm{Fe}}_{0.26}{\mathrm{Ni}}_{0.74}{)}_{50}{\mathrm{B}}_{50}$ ferromagnetic amorphous nanoparticles. Our results show evidence of the surface contribution to the magnetic properties in the $M(H),$ $M(T)$ and relaxation measurements. We observe a large increase in the magnetization with decreasing temperature, a nonsaturated component in the $M(H)$ curves, the presence of two maxima in the zero-field-cooling $M(T)$ data, and two viscosity regimes in magnetization relaxation data. The results have been interpreted by a simple model where we consider each single-domain particle as a core plus shell system with a uniaxial anisotropy acting on the core and a surface anisotropy acting on the shell. Monte Carlo simulations based in this core-shell model qualitatively reproduce all the observed phenomena.