Hello, depends on the test centre. There is usually a place for personal belongings, but unlocked so I wouldn’t leave anything too precious. In Frankfurt there was a supervised desk where you could leave your mobile phone though. The test centre in Frankfurt can be freezing in December…there it is definitely best to go for the onion-look. If it ends up being warmer than you thought, you can always take the top layer off. If you think the test centre were you are sitting the exam might be cold, I would also recommend staying away from sneakers with rubber soles - my feet were FREEZING two years ago. There are water fountains available in the room - so you can get something to drink.
I guess it depends on the test center. In London, water and bathrooms are available during the exam and there is a massive storage area for belongings. You can always bring a padlock and lock your bag and keep your phone in the bag or give it to the proctors (if they allow it).