A dog that is shivering hard, and unusually lethargic, needs warming up promptly.
Most dogs cope well with cold weather if they keep moving, but a few things are worth keeping in mind before a winter walk.
Grit and paws
Road salt and grit can irritate paw pads, and can be mildly toxic if licked off in any quantity. Drying or rinsing paws after walks on gritted roads helps, and paw wax is worth considering for a dog prone to irritation.
Knowing when to turn back
Thin-coated, small, older, or unwell dogs can lose heat faster in cold weather. Shivering, tucking the tail, or clearly wanting to head home are all signs to turn back rather than push on to finish the usual route.
Signs to watch for
Plan the length of a winter walk around the return leg, not just the outward one. A cold, wet, tired dog can be more at risk on the way home than on the outbound route.