Accurate estimates of wind speeds at wind turbine hub heights are crucial for both wind resource assessment and day-to-day management of electricity grids with high renewable penetration. In the absence of direct measurements, parametric models are commonly used to extrapolate wind speeds from observed heights to turbine heights. Recent literature has proposed extensions to allow for spatially or temporally varying vertical wind gradients, that is, the rate at which wind speed changes with height. However, these approaches typically assume that reference height and hub height measurements are available at the same locations, which limits their applicability in operational settings where meteorological stations and wind farms are spatially separated. In this paper, we develop a two-step spatio-temporal framework to estimate turbine height wind speeds using only open-access observations from sparse meteorological stations. First, a non-parametric generalized additive model is trained on reanalysis data to perform vertical height extrapolation. Second, a spatial Gaussian process model interpolates these hub-height estimates to wind farm locations while explicitly propagating uncertainty from the height extrapolation stage. The proposed framework enables the construction of high-resolution, sub-hourly turbine-height wind speed time series and spatial wind maps using data available in real time, capabilities not provided by existing reanalysis products. We further provide calibrated uncertainty estimates that account for both vertical extrapolation and spatial interpolation errors. The approach is validated using hub-height measurements from seven operational wind farms in Ireland, demonstrating improved accuracy relative to ERA5 reanalysis while relying solely on real-time, open-access data.