I'd say it's 80% attitude and 20% proper clothing.
I used to cycle only during dry days in spring, summer, and fall - my main worry was getting wet, and winter seemed quite extreme in Finland where I come from, though I imagine it's probably quite similar to Scotland. Then one warm summer day I misjudged the weather and ended up getting totally soaked on the way to work, but it felt more refreshing rather than annoying. I'm sure having showers at the office helped there. From that day on rain didn't really bother me and I cycled every day in summer. When it's pouring water already before leaving it does take some convincing to hop on a bike in shorts and t-shirt, but you get over it.
Now, with the worry about water out of the way my thinking shifted towards keeping warm instead. Yes, waterproof clothing definitely helps there. I go myself lightweight waterproof, not very breathable, jacket and trousers. They kept me dry, and layer(s) underneath kept me warm enough to commute all year, even in -10C or so (I vaguely recall at -15C it started to get a bit too chilly to breath heavily) and quite a bit of snow.
Nowadays I'm cycling all year in London and I've traded the waterproof jacket to water resistant windbreaker (more breathable and visible) and kept the trousers for worst rain (it doesn't really rain in London, it's just heavy mist.) If I misjudge the clothes on the way out and get soaked on the way, then I get soaked, big deal. Granted, having warm shower waiting at the office definitely makes things easier.
Still, I'd say it's mainly in the attitude.