Studs only really help with "solid" stuff, ie ice or compacted snow. For anything which is mobile, ie fresh snow or slush stuff, you want something with grip ie traditional treaded tyres. You can get heavily treaded tyres with studs as well, which are useful in environments with a mixture of conditions or cold enough that the snow stays more mobile than it tends to in the UK.
I didn't really see much on the way home. On Clapham Common there had obviously been a bit of snow, but helpfully the wind had blown it to one side of the cycle path. Around Tooting Bec there had been more, and the geography of the area reduces the amount of wind, so there were patches. The glint of shinyness in the front light often doesn't tell you if there is just the barest hint of ice, or significant patches, so around there I was somewhat circumspect with my speed, and took it carefully.
A few miles from home it did start snowing with a little bit more effort, and it was just about sticking to the roads when I got to Croydon. Whether there will be anything more significant overnight I doubt. The weather radar doesn't show much coming this way, and it's moving slow enough that even if there is anything significant coming this way from the continent, if it's not on the radar, it won't hit for quite a time (ie until tomorrow morning).
At the moment I certainly can't be bothered with the faff of swapping over tyres. The forecast doesn't suggest will have anything worse than the occasional wintry showers for the next few days, it's just forecasting it to be too warm for anything to last around here.