Exercise does warm up the body but not for crazy extended amounts of time. Usually one can feel the affects of a workout for up to an hour depending on if you rest or keep moving and how intense the workout is.
I believe your question is; "If I work out before a walk, will my body stay warm?"
That's how the question looks to me but I may be wrong.
The answer is: Yes, if you have an intense workout and then go on a walk, your body will stay in workout mode and keep burning calories, keeping you warm during your winter walks.
I hope this helped.