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Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.