No problem.
The unpredicatable nature of weather in Scotland means that if it looks bright and sunny in the morning, you still need to leave your house with a jacket because you cannot guarantee that it won't rain heavily later in the day. Depending on when you take lunch or arrive at work, some people will be drenched, some will enjoy clear skies and sunshine. This isn't necessarily like this every day, but prepare for variability.
The dry air in the winter can make dry your skin, so moisturise well. It can also get windy.
That said, it's fairly temperate. The weather usually goes as low as minus single digit celsius, and as high as sub-30 celsius. And compared to other locations in Scotland it rains a lot less.
https://www.climatedata.eu/climate.php?loc=ukxx0052&lang=en
With regard to Brexit, it's hard to know where to begin so I'll recap and potentially editorialise.
The Conservative party (popular right wing political party), which is currently ruling as a minority government, has historically been split on the subject of integration with Europe. One side likes banks, free trade, free movement and big business and doesn't mind a bit of bureaucracy (pro Europe); the other likes deregulation, sovereignty, controlled immigration, "brass plaques", and small/medium business (anti Europe). This argument led to a polarising vote to the populace about whether we should leave the European Union or not.
Joining the European Union, which the UK did in the 1970s, was initially about centralising trade agreements. Now though it has a common currency (though the UK retains its own independent currency), legislates and regulates on many varied aspects of life and business, and takes huge membership fees and pays out lots of grants. Some see this as a good system even if reform is needed, some absolutely hate this with a passion.
The public vote polarised the country greatly and ended 52%/48% in favour of leaving the EU. Even if the result was conclusive the fact it's within a rounding error, the winning side committed electoral fraud and made lots of promises which they instantly backed down from, and there's evidence of Russian intereference, so there's a lot of bad feeling from both sides as many can't accept the result as final.
The key take away is that the UK has had 2 years to negotiate leaving but being in the EU affects so many aspects of life, that almost nothing has been decided and there remain so many grey areas. The worry now is that no deal will be reached and leaving the EU without a deal creates massive legal uncertainty in almost every industry conceivable, and means all trade between UK and the rest of the world (currently done via EU trade agreements) will instantly get WTO tariffs - in effect putting instantaneous costly barriers to all goods and services.
At present we're hoping politicians will become sensible and sort something out that doesn't plunge the country into financial ruin, but it's the uncertainty that's the problem at the moment.
Add to this, many in Scotland wish to be independent (another similarly polarising issue) and feel their wishes regarding Brexit are being ignored by the UK government (Scotland in comparison to the rest of the UK wanted to decisively remain in the European Union 62%/38%).
So in conclusion: (a) there's a lot of uncertainty about the UK leaving the European Union in spring next year and what this will do to the smooth running of the country (b) if the UK does leave in a crash and burn style, that may lead to renewed calls for Scotland to become independent and who knows what that will look like. Caveat emptor.
(and for full transparency of my personal bias: I'm pro European, anti Conservative party, pro Scottish independence, and was on the 100,000+ march for a 2nd independence referendum at the weekend)