The weather will vary from about 8degrees to minus2 degrees (Celsius, because its the UK). It can be a bit more extreme with temp, but generally cold, it doesn't rain that much in winter, except when it does....
sometimes it snows, but not proper snow - just enough for car drivers of 4x4s to stay over confident and write off their shiny Range rovers.
Fog is a big thing, so head torch. You'll want that anyway because it's dark most of the day which is short, and our councils turn off the street lighting to save money at night.
Tights, windproof and waterproofjacket, layers.
Road shoes need grip, it'll be wet, and we have more potholes than you could imagine.
Doing XC - 15mm spikes. Vest and short shorts. You're going to get wet - we run through rivers, puddles, streams etc.?
Trail runs? Dress for XC, with trail shoes - think big lugs... You'll still slip around, but you'll be more confident about it.
I'm in Lincolnshire - it's flat, and therefore when the forecast says only 4mph winds, we get 20mph. Its always a headwind.