The colours for winter are burgundy, forest green and dark muted Jewel colours. Summerish pastel walking sticks don't necessarily go with Autumyn/ winter clothes. I like using metallic sticks. What sun there is glints off it, brightening it up and they add a pop of colour to muted winter palettes.
The sticks I have selected range between £20 and £179 for the teal metallic Derby stick (Amazon). The burgundy one is usefully as it collapses in to 5 sections so will be more compact when folded up. I also think it is a beautiful Autumn / winter colour and would look great against black boots or black winter coat. The metallic blue stick with a black handle is unusual as it has a soft handle which is easier to hold if you have neuropathic or arthritic pain in your hands.
Jewellery or clothes wise all these sticks look great with dark jewelled colours or black. Quartz necklaces in the same shade would bring out the colour of the stick and bring the whole outfit together.
Stick pictures are my own or stock pictures taken from Amazon.co.uk and healthandcare.co.uk