Thresholds of convection excitation and nonlinear convective flow patterns in a horizontal colloidal-mixture layer heated from below are investigated. We take into consideration the fact that, provided the barometric stratification has been reached prior to imposing the temperature gradient, only oscillatory disturbances develop. The influence of separation ratio, sedimentation length, and Prandtl number on the thresholds of oscillatory convection is studied. To examine the complex nonlinear dynamics of the system, numerical simulations with realistic boundary conditions have been carried out using a finite difference method. Long-wave and cellular instability modes as well as transitions between the conductive state and the traveling-wave regime are discussed. It is shown that the traveling-wave regime is stable within a specified range of heating intensity (the Rayleigh number interval). Complex bifurcation and spatiotemporal properties of dissipative structures caused by the interaction of the gravity-induced concentration gradient, nonlinear advection, and mixing of the fluid with nanoparticles are considered.