Hi,
You can get a child's coat from regatta. If you search for waterproof breathable you will find something good.
You need thermal vests to keep warm. You wear them under your clothes.
My ds would usually wear a t-shirt, then a long sleeved t-shirt, then a hoodie and a breathable waterproof coat on top.
I wear the same except my coat is padded so i don't need the hoodie. I wear normal trousers with over trousers on top to stop the wind going right through. It keeps me much warmer overall if my legs are warm. We all wear leather ankle books all the time. We have no other shoes except sandals for winter. We get them from Ecco.
We also need hats, scarves and gloves in the winter otherwise we wouldn't be able to leave the house. We live near London.
If you get cold at 22 then you may find it a bit of a shock to be in sub-zero temperatures, especially when jetlagged. It might be good to bring melatonin if you can buy it there.
If you can fit a hot water bottle in your luggage that will help, and if not then when you are here you can just get any plastic drinking bottle and fill it with hot water from the tap and hug it in the evening. That will make you feel warmer. I used to do that when travelling.
Good luck with your holiday.