I did my CPL in Scotland, looking back through the logbook about 30hrs flying in Oct/Nov, that was with lots of ground school/exams taking up time, so it is possible.
You get a good mix of “educational” weather up north but it seemed less common to get total non-flying days compared with similar places in England, for instance. Cloudbase and visibility are the two main problems with learning to fly and the western side of Scotland is normally OK with both, even during the winter. It can get pretty windy but that’s helped if you have a choice of runways.
Even at the end of November, you’ve still got >7hrs of daylight to play with. You get snow on the hills but very rarely at sea level.
As you say, the odds are somewhat against you to complete the entire syllabus in a 4-5week period in Scotland but you never know. It is very much my opinion that intensive instruction/practice is pretty much the best way to learn anything and getting a good blast of continuity will set you up much better than to attempt to do it piecemeal over a much longer period of time. Also, Scotland is a fantastic place to go flying as the sky changes hourly and the scenery is amazing.
If you have the time and the money (which rarely coincide for most people) why not give it a go?