Supporting wine production operations in an increasingly global market has grown ever more challenging. Export-focused wineries supply many foreign clients, often requiring different labels for the same kind of wine. Order forecasts tend to be highly inaccurate, and wineries must be able to quickly react to changes, making lot-sizing an important consideration. One tool to reduce product misallocation is postponing product differentiation, where the natural decoupling point for premium wine is the labelling process. However, the double handling involved incurs additional costs and time penalties. We analyse the performance impact of postponing the labelling of bottled wines by developing a multi-stage mixed-integer stochastic programming model with full recourse for demand scenarios. The underlying data and policies are based on an unnamed Chilean export-focused winery. The model supports lot-sizing under several winery production policies. We experiment with different levels of capacity tightness, demand variability and demand correlation between wines, optimising for reducing order backlogs, inventory levels and line set-ups. While we find that some amount of postponement will always be recommended, the exact mix and degree depend on these external factors. Postponement has the most benefits when production capacity is moderately tight, demand variability is high and wines have negatively correlated demands.