Winter tyres on a road bike is an interesting topic. Firstly 'winter' is such a weird concept these days so we'll include all times when it's not dry and sunny!
Requirements:
1. Good grip in the wet: For this you need a completely slick, soft compound tyre. Tyre tread only makes grip worse as it reduces the rubber contact area with the tarmac. Knobbly mtb tyres are worst for this where the chunky knobbles also distort under load, although their bigger size compensates to a degree.
2. Toughness and puncture resistance. In winter there is more crap on the road and fixing punctures is even less pleasant. Kevlar belting and more rubber (= heavier) do help, but again tread pattern can make matters worse. (traps flints and bits of glass in the part of the tyre that is thinnest). Kevlar inserts can also be added to ordinary tyres. Also if you do puncture, you want a tyre that allows you to change the inner easily. Some tyre / rim combinations are a pig in summer. With frozen fingers they are even worse. This for me eliminates some people's 'favourite' winter tyres.
3. Grip on mud, shoot and leaves: If your rural commute (or cycle path) is so crappy to be almost 'off road' in character, then an off road tyre might be good. But for a 'knobbly tyre' to work, the surface has to be soft enough for the tread to 'dig in'. This is not the situation with a layer of leaves or muddy run-off on tarmac. Compromise (dual purpose) tyres will quickly choke up with mud and becoming good for nothing.
4. Wet man hole covers and painted areas: Again, the softer the compound the better, but realistically avoid these if possible or treat with care.
5. Ice: Nothing will help except tungsten studded tyres (they are available). When a ground frost is possible, proceed with caution and stick to gritted roads.
6. Snow: If the snow is soft enough for a knobbly tyre to make an impression, then snow riding can be fun. But in towns, other traffic will quickly 'roll' the snow down to white ice and the fun is over.
So I use Mich Pro Race 25c's on my winter training / audax bike and Panaracer Pasellas 32c's on my commute / touring bike. And in summer - I use exactly the same.