This article was only supposed to be an overview. If I covered everything, I might as well have written a book.
Medicine, food, spare parts, etc, can all be stocked up before the war actually happens.
I'm sure if there is ever going to be a nuclear war, everyone will be notified about it in due time. If not, the escalation towards the disaster alone will prompt a lot of people to prepare and stock up way before it happens.
Plus, it is usually one specific country that gets targeted first so if you live in another country, you'll be given at least a few days to prepare for the oncoming disaster.
Also, I'm pretty sure you already know the answer to "How you going to keep warm during nuclear winter?"
Hint: electric heater (shhh, don't tell anyone)