I am happy to hear the river flow forecasts performed well so far. You have to realize that the influence of snow accumulation in winter, and snow melting in spring/summer, is explicitly accounted for in our forecast. In fact it is a very important source of the skill we see. Based on precipitation and temperature (corrected for altitude, see below) the model continuously computes the thickness of the snowpack (in so-called snow-water equivalents). Based on that we have a fairly good idea how much snow there is in any basin at the start of a forecast. This so-called inital condition provides so much ‘memory’ to the system that it allows the model to predict snow melting and therefore river flow in spring/early summer fairly well. In fact the (poor) quality of the precipitation forecast becomes less important, especially when -like in your basin- in the melting season the rainfall is relatively low.
Further you mention that temperatures are overestimated. I dont know compared to what reference, but of course temperature is very sensitive to altitude. So if you compare predicted temperatures to some mountain weather station data, there will generally be a systematic bias. A bias that is fairly constant and that can easily be corrected, if we know the difference between station altitude and model terrain elevation. Having said that temperature anomaly forecasts are generally much better than precipitation anomaly forecasts, I would expect so too in you region. Note that I say ‘anomalies’: they are by definition not senstitive to systematic errors!
Finally, to connect what I said in the previous two paragraphs: for snow accumulation and melt our models work with altitude bands. So even if your basin is represented by only a few model units (sub basins in the EHYPE, grid cells in may other models), within each unit the models keep track of different altitudes with each a different temperature to account for the unresolved topography of the mountains.