You can ride a std race bike in winter but...
In UK winters, the roads are usually wet and rarely icy. Mudguards/fenders are really useful. You may be able to squeeze some SKS raceblades into your frame.
Ideally you need clearance for 28mm tyres (min) + some proper full-length mudguards (SKS Chromoplastic).
For clothing, you need some tights over your shorts, a long-sleeved jersey, a windproof and some insulation (eg thin wooly jumper). You need thicker socks than for summer, full length gloves and a neck-warmer.
Some people use neoprene booties with clipless pedal systems.