Motivated by the need to capture statistical properties of turbulent systems in simple, analytically tractable models, an ensemble of Gaussian sub-ensembles with varying properties of the correlation function such as variance and length scale is investigated. The ensemble statistics naturally exhibit non-Gaussianity and intermittency. Due to the simplicity of Gaussian random fields, many explicit results can be obtained analytically, revealing the origin of non-Gaussianity in this framework. Potential applications of the proposed model ensemble for the description of non-equilibrium statistical mechanics of complex turbulent systems are briefly discussed.