A new snowflake aggregation model is developed to study single-scattering properties of aggregate snowflakes. Snowflakes are generated by random aggregation of six-bullet rosettes constrained by size-density relationships derived from previous field observations. Due to random generation, aggregates may have the same size or mass, yet different morphology allowing for a study into how shape influences their scattering. Single-scattering properties of the aggregates were investigated using discrete dipole approximation (DDA) at 10 frequencies. Results were compared to those of Mie theory for solid and soft spheres (density 10% that of solid ice) and to T-matrix results for solid and soft spheroidal cases with aspect ratios of 0.8. Above size parameter 0.75, neither the solid nor the soft sphere and spheroidal approximations accurately represented the DDA results for aggregates. Asymmetry and the normalized scattering and backscattering cross sections of the aggregates fell between the soft and solid spherical and spheroidal approximations. This implies that evaluating snow scattering properties using realistic shapes, such as the aggregates created in this study, is of paramount importance. Concerning the morphology of the aggregate snowflakes created in this study, the dependence of their single-scattering properties on each aggregate's detailed structure seemed of secondary importance. Using normalized standard deviation as a measure of relative uncertainty, it is found that the relative uncertainty in backscattering arising from the different morphologies caused by random aggregation is typically ~15% for individual particles and ~18% when integrated over size distributions. Relative uncertainties for other single-scattering parameters are less.