Combine vinegar and milk in a small Dutch oven, stirring well; add sugar and syrup, stirring well. Slowly bring to a boil, stirring until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and continue cooking, stirring occasionally, until mixture reaches soft ball stage (232°).
Remove from heat, and cool to lukewarm (110°). Beat with a wooden spoon until mixture is creamy and begins to thicken; stir in walnuts. Working rapidly, drop mixture by tablespoonfuls onto waxed paper; let cool. Store in airtight containers.