In case of Slovenia, and often for other regions and countries as well, the land cover labels are provided on a yearly bases, and can be updated every few years. This means that for a given location the seasonal changes are not taken into account, and the label describes “what is on land most of the time”. For the majority of classes this is not a problem (e.g. built-up area, grassland, agricultural land), although it might be source of noise for others (as you mention rivers that dry up or flood, bareland on mountains).
It is up to you and the model to try and deal with this, either by letting the model learn these variations, or removing them from the input data (e.g. only provide summer-time months).
The snow class refers to permanent snows or glaciers if I remember correctly, so snow/ice present all year, which is quite rare. This becomes then a problem of imbalanced class labels, which you’d have to handle separately by, for instance, stratified sampling.
In addition, there is often a land cover/land use source of noise (e.g. land cover marked as build-up which actually denotes use, and might actually be grassland where houses/buildings could be built on).
Good luck with your efforts.