I used to wear over-trousers in the winter on my commute. They won’t save your feet though. Overshoes are the only thing to save your feet. Someone will be along and go “winter boots and sealskin socks”, but they still have wet shoes and socks, and it’s horrible putting them back on at the end of the day if you don’t have somewhere to dry them properly.
Unless you’re riding at a pace to match the club run then I always preferred to wear decent waterproof kit. I would ride in baggy shorts with padded boxers spring-summer-autumn, with the over-trousers and overshoes in my bag. Warm days and summer I’d wear a jersey or t-shirt, Spring and Autumn would be a longsleeve jersey, with a lightweight waterproof jacket, again in the bag. As soon as the jacket was on more than off I’d switch to base layer and winter jacket, base layer leggings and wear the over-trousers whatever the weather. It would be cold by then so the idea was to keep warm. I’d only be carrying the overshoes in the bag then. I did have excellent drying rooms, so warm dry kit to ride home in.
A couple of winters would kill a pair of overshoes, but at £15-20 it was cheaper than killing an £80 pair of shoes. Cheap, comfortable, warm, and dry. Leave the team kit for posing with the roadies. 😉