Snow is easier to dress for than cold rain, because it is dry. What makes you cold is sweat on the way up and wind on the top (sample guide).
Start with a merino or synthetic base layer, never cotton. Add a fleece or a light down jacket, and a waterproof shell over it all. Take the middle layer off on the climb and put it back on before you stop.
Carry a spare pair of socks in a bag. Wet feet are the first thing that makes a winter walk miserable, and a dry pair at lunch fixes it.