I think that travelling so far, in a perhaps unreliable vehicle (comment above, not sure if you think it is though ? ) at this time of year, and more importantly, in this kind of weather,
Temperatures across the UK have dropped and cold weather is forecast to continue into next week.
www.bbc.co.uk
might not be the best idea. Even if it is for something you really want to attend.
I'm presuming it's the experimental archaelogy conference in Edinburgh ?
Put it this way, I live nearby and I'm not driving into the madness that is Edinburgh for the conference.
Parking is a nightmare, and expensive. Hotels and B&B's etc., are ridiculously expensive there too.
Normally I'd have said you'd be better coming by train, but there are train strikes just now too.
The journey north though. Well you have to get up to and over the Border, after you've driven up the spine of England. I know it's a busy well travelled route, and just now is being gritted/salted etc., on a constant basis, but it's still not fun driving, especially when you get to the hilly bits at the Border.
If you're not feeling well, you know that's not a good time to be driving anyway. There will be other conferences, and this one is going to be hit by so many things. From the bad weather, to the time of year, train strikes, etc.,
I think the others have already given really sound advice on what to pack in the car for emergencies.
I would sincerely add that some kind of Rescue service, and a fully charged mobile phone are necessities.
AutoNationalRescue have brought us home from some truly wild spots when the car broke down. No fuss, no bother, very reasonably priced.....and they answer the phone
They use a network of local garages rather than dedicated specialised vans.
Best of luck with it, whatever you decide.
M