Games are not considered canon and if there's no mention of the reason for wintering in Kaer Morhen, then there's none. That leaves out-of-universe explanation and Gallifreian did superb job.
As for books there is implicit meaning for spending winter in Kaer Morhen for witchers - this is their break from work (partly due to conditions, but mostly due to lack of work), the Keep is their home where they can feel safe and relax (for the values of relax) and there is need to stock back up on equipment and inventory (with potions being most important), make repairs and exchange knowledge, experiences and spend time with "family".
Potions are important to mention: some of them can be made only in Kaer Morhen from ingredients not found elsewhere and obviously instructions for making them are in the Keep's library.
Last point. Book(s) strongly suggest that there is only one place where witchers come from: Kaer Morhen. Different Schools are more like japanese dō, which translates loosely as "The way". They should be looked at like different learning tracks, rather than in terms of different locations and making them different sources of witchers is canonically unsupported.