As others have said, get a 'proper' padded coat, not a fashion one. You need something that will keep the rain/sleet/snow out, as well as the cold. Synthetic insulation can sometimes be better than down for wet cold - it keeps working in the wet. Rab, mentioned by others, is an excellent brand. Trespass is good, too. Mountain Warehouse do very good thermals and bargainous merinos, but I've never been impressed by the durability of their outer layers. Didriksons for spring/autumn wet weather are IMHO unsurpassed. And they have hoods that stay in place in wild winds! I also like some of Rohan's stuff, though it's not cheap. Schoffel is very 'huntin',shootin', fishin' ' and costs a bomb, but has a good name.The socks I like best are by Bridgedale. Vastly expensive but very comfy and last years.
If you're going to be working outdoors then you'll need damp-resistant trousers (Rohan and other top brands do these) and/or waterproof overtrousers. These latter are wonderful when it's really wet, but invariably hot and sticky after a long day. Personally, I find wellies no good on damp rocks or black ice; you need decent boots and - if working on snowy/icy steep slopes - possibly something like YakTraks as well.
I've mentioned this before on Mumsnet, but keep country legwear to the straight and narrow; no flappy fashion jeans, except in towns.
Perhaps your phone has a good torch, but if not, get one that's bright and lightweight and long-lasting. Plus a spare. It's already dark enough up here to need one - so that any traffic can see you - when walking along narrow unlit country roads. If you're off-road, then you'll need one even more to see where you are going.
Just looking at my everyday winter wardrobe:
*Lands End silk underwear
*Bridgedale and Craghoppers socks
*Mountain Warehouse thermals/Lands End long-sleeve tee shirts
*As much merino knitwear of various shapes and sizes as I can afford. Mohair/alpaca are both very warm, but I find them unbearably itchy. Ditto most pretty FairIsle lambswool.
*M and S cosy jeggings - perhaps get one size too big if you want to wear tights or long johns underneath. They are warm, comfortable, wash well (mud!) and are long-lasting. Other companies - eg Acai -do posher versions.
*Didricksons waterproofs; Rohan ditto (old). Also various old anoraks for gardening or other outdoor work - Regatta, Brasher etc.
*Rohan long and lightweight padded coats with hoods. I wear a very old one of these indoors, just like medieval people used to put on a fur lined robe to sit down to read or write.
*Scarves of all kinds
*Gloves (always get wet, so take a change or two if planning gto be out and about all day). You can get posh waterproof ones, but I find them clumsy.
*Footwear - Ecco and Josef Seibel for town; for the country, Karrimoor, Merrell or whichever 'proper' brand suits your feet.
*Am not keen on hats, but I do have a fake fur one which is surprisingly warm and weatherproof.
All that is just my personal taste. You'll soon find what works for you. If you're going to be in a town, then a lot of the above won't apply.
It's often not very, very cold here, but (IMHO) damp West Highland cold and grey can be more chilling than freezing but sunlit Alpine snows.