I have a Stanley toolbox with my general kit. More for dealing with things stuck in the car. First aid kit, plastic gloves, pair of work gloves, WD40, the inflatable can of stuff for punctured tyres, straps for the roof bars (DH helpfully threw those in recently!), a decent torch with a good worklight side, some pocket packs of tissues, a couple of mini bags of Haribo. I have tape, a swiss army knife, and boiled sweets, suncream, lip balm, tissues, hand sanitiser etc always in the glovebox/car door. And a large bag of shopping bags also lives in the boot that can be appropriated for other uses as necessary.
I had more in terms of long life food items, but they kept getting eaten by DD. I also had water but it was drunk (multiple times) and I haven't replaced it yet.
When I am going farther afield, I usually make sure I have a blanket, extra hat and gloves, etc. And in poor weather, snow socks, and making sure stocks of food (snacks) and water. But I tend to be quite local these days.
When we have poor weather though, I bring a nice pair of shoes to work and travel in my decent foul weather gear (rain or snow gear, depending on the needs) and either snow boots or proper hiking boots - I have thought about my sailing boots once but it's never been so wet that it was necessary. Spare socks in my desk always, and an extra pair in my backpack on bad days.
My everyday bag for work is a North Face laptop backpack, and I have a waterproof cover for over it (and depending on whether I've recently travelled internationally or not, has reasonable emergency kit in it but may not currently have the swiss army knife). My everyday coat is a long Ilse Jacobsen raincoat. Because I commute by train and the platform is on the coast and bitter and occasionally very wet; and then I have a bit of a walk after that.
I have well worked out alternative routes for different kinds of bad weather - snow means 1 route involving buses; rain (of the catastrophic and flooding level) usually means driving so I have control. If I had to abandon the car, I would be happy walking long distance.