Best winter tyre I ever used for stickiness was Pro race3 but they cut up easily but mrs K has had one on the front wheel for the last year and a half, People widely rate gp4000’s so they’ll be ok. I use a mis- match of those, michelin lithions, schwalbe blizzards and on various bikes and they’ve all been much ok. I ride 23’s except on the fixed commuter which has 25’s on it but then I ride Surrey mainly and there’s a fair amount of gravel, leaf mulch and general slime whereas you seem to have something like the Somme nearby 🙂 You could go up to 28’s or more if the frame will take them, not sure about cx tyres never used them.
Not wishing to patronise, you probably know all this, but with mud and crap on road firstly try and ride around, if not possible smooth straight lines, no sudden braking, death swereves etc,, try like on a hardtail not to tension up, let the bike geometry work. For me with any threat of ice, don’t road ride seen a clubmate, early 30’s break a hip; one replacement op already and they’ll be more as he ages -go mouuntain biking.
Hope it goes well.