Previous studies have shown that the effects of climate change on building structures will increase the mould growth risk of the wood-frame building envelope in many circumstances. This risk can be controlled by wind-driven rain deflection, improving water tightness of the exterior facade, and improving cladding ventilation. However, the effectiveness of these risk mitigation strategies are subject to various uncertainties, such as the uncertainties of wall component properties and micro-climatic conditions. The objective of this paper is to apply stochastic hygrothermal simulation to evaluate the mould growth risk of a brick veneer-clad wood-frame wall with a drainage cavity under historical and future climatic conditions of Ottawa, a Canadian city located in a cold climate zone. An extensive literature review was conducted to quantify the range of stochastic variables including rain deposition factor, rain leakage moisture source, cladding ventilation rate and material properties of brick. The randomised Sobol sequence-based sampling method, one of the Randomized Quasi-Monte Carlo (RQMC) methods, was applied for risk assessment and error estimation. It was found that, under the climatic condition of Ottawa, limiting the amount of wind-driven rain to which walls are subjected is a more robust mitigation measure than improving cladding ventilation in controlling mould growth risk, the improving of water tightness of exterior façade is not as robust as wind-driven rain deflection and cladding ventilation, however, the reduction of rainwater penetration can reduce the mould growth risk at different levels of rain deposition factor and cladding ventilation rate.