Your current bike is fine for winter use. You need tyres for your local winter conditions. For cold damp you need a touring style wider tyre (you may have this already). Studded tyres are for ice and snow.
Full length fenders are best for wet but can clog in the snow. Clip on fenders often work better in snow.
Clean and wax your frame before winter. Ensure that the hubs are fully lubed. Grease your cables and any metal-metal contacts and threads (seatpost, pedals etc). Im not sure if you grease the stem/steerer interface on a threadless system; I do on my old quill stem.
Pick a chain lube that is easy to apply in the cold and doesnt wash off.