We describe smooth non-stationary generalized additive modelling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. Fitting is by maximum penalized likelihood estimation, with uncertainty assessed by using differences of deviances and bootstrap simulation. The approach is illustrated by using data on extreme winter temperatures in the Swiss Alps, analysis of which shows strong influence of the north Atlantic oscillation. Benefits of the new approach are flexible and appropriate modelling of extremes, more realistic assessment of estimation uncertainty and the accommodation of complex dependence patterns.