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If it's mostly for riding through London I would probably not consider snow conditions in the equation given how uncommon they are and how specific the tyre choice would be. Although a file thread would probably be fine for powdery snow and roll nice year round.
I commute on conti 4 seasons and never had an issue. Looking at replacing them with Marathon Almotion Evo when they are done
City riding through London - mainly commuting to work every day.