I would add my suggestion that adding wind pants over trousers might help more, or long underwear/tights under the trousers. Wind pants can be removed indoors. At the same time a jacket should be tight around the waste or hips with a drawstring to prevent air coming up inside. A long coat always allows lots of cold air up the inside. An alternative is snowmobile or outdoor construction overalls that are a one piece garment from head to toe, but keep the cold air out and don't have to be tight at the waist.
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In fact the more I think about it, a person who gets cold and especially cold legs dog walking might be best off in a snowmobile suit. So this is really an adult version of putting kids in snow suits, and kids relish playing in snow and ice almost forever it seems.
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I was visiting a friend once on a long trip and we planned to do some mountain hiking in the winter but didn't have all the usual outdoor gear along. So he just said put on two pair of pants. It was a bit awkward but worked very well.