Speaking of wind driven rain...
I was in Northern England and Scotland from mid to late May last year. It was cold and rainy much of the time. Layers are the way to go, but I didn't do a very good job of that.
I can't wear wool, so I packed multiple thin layers of synthetics. Not warm enough! I should've taken fewer items and had more fleece.
This is what did work for me.
A fleece beanie style hat and gloves.
An Eddie Bauer women's Mackenzie trench coat similar to this one. It kept me dry all the time and warm in some situations, but not in the worst of the weather even with multiple layers underneath. The beanie helped keep the hood on. I never use an umbrella.
prAna men's Stretch Zion pants like these. These are not rain pants, but they dry out very quickly. I got men's because the women's similar pants had totally useless pockets. TSA alert: they were fine going through security at Tucson, but they set off bells at security in Seattle. I no longer wear them on the plane.
Two pair Cuddl Duds long underwear tops and bottoms. The bottoms were great under any of my pants. The tops were a very helpful base layer. They doubled as pajamas. They are lightweight and low volume for packing. That's important for me because I travel carry-on only.
Ahnu Montara boots like these. My feet never got wet or cold in spite of rain, wet grass, mud or puddles.
Sockwell circulator socks. These do have a bit of wool in them, but oddly, I'm not bothered by it. These are very good for long hours of walking or standing as well as for long hours sitting, like on the plane.
Do not underestimate how bad the weather can get or how quickly that can happen -- especially if you are outdoors. Be aware that indoors may not be as warm as you would like and that you may not be able to have any influence over the temperature at all.