4 years at University in Edinburgh gave me a good feel for the weather. Frequent business trips nowadays show it hasn't changed!

You don't get much snow in Glasgow or Edinburgh (maybe once or twice a winter, and it doesn't last long), but you get a lot of cold rain and (especially in Edinburgh) wind. It can be pretty bleak. [Current weather right now at Edinburgh Airport is 5 degs C and showers - fairly typical]. A further consideration is that in December it starts to get dark in Edinburgh at about 3.00 pm. If you want to maximise your daylight (a useful commodity for sightseeing) you are right to go as late as possible in March, if possible after the clocks change. By June, BTW, the converse applies and it is light until well after 10.00 pm.

Edinburgh particularly is a spectacular city to just walk around and absorb the atmosphere, day or night, so it's a real shame if the weather is poor.

By the way, that radio station remeniscence reminds me of another one from BBC Radio Scotland one day. "You've been listening to (xxxx). And now for the weather. Rain. And now for the next programme ...."