4 km is not far.

My current commute is 10 km one way; a bit longer than yours but still in the short-ish category. My previous commute was 4 km.

On dry snow-free days I just wear whatever pants I'm going to wear at work.

On rainy days that doesn't work. Legs get a lot wetter in the rain when biking as opposed to walking since a lot of the pant leg's surface area is exposed to rain in the middle of the pedal stroke. And even with fenders water and dirt splashes up. So on days with rain, slush, dirt, sleet, snow, road salt etc. I still wear whatever I'm going to wear for work with a pair of waterproof climbing pants over top. I tried cycling-specific waterproof pants and they never fit well. But the climbing ones are amazing: tough, fit loosely over any other pants, keep me completely dry and allow for great freedom of movement. They were something like almost $200 on sale when I'd bought them some 7-8 years ago, and I can't imagine my life without them. Should work very well for BC.