Before lockdown and all this working remote shenanigans, I used to commute daily into London year-round. I would only stay home if it was thick snow... TBH London never got that bad, rarely much below 0C, and all the main roads were gritted and kept clear. It was only the small side streets at work and outside my house that would be left with snow on them.
It's just about getting the right gear. Gerbings heated gloves are amazing, then just partner with decent textiles, themal liners, Merino wool base layers etc. All make a cold weather ride manageable. On a clear day it can be very enjoyable. It's only when it's coming down with cold rain, sleet and snow on you does it get a bit miserable and you get some serious visibility issues.
As the old saying goes "there's no such thing as bad weather, just bad choices of gear"