I have been to Glasgow in January - I took an overnight train up there from London, and was met by my dear old boss. It was a cool grey day, just a little rain, but there was plenty to see and do indoors as well. It was a very nice visit, but then, I did have "native" guides! And his wife even let me try a bite of her haggis at dinner, too.

The British rail system is a bit unpredictable, schedule-wise, but will get you there reliably, as long as you aren't on too strict a timetable.