Don't know for sure, but I doubt Winnabego ever built bikes. Usually a company like John Deere that doesn't build bikes will contract with an Asian firm to build x number of bikes with their name in decals and/or headbadge.
Usually they are bottom line bikes which has made many of us wonder why a reliable company that produces a quality product would put their name on a cheap bike!
As stated, I don't know the lineage of your bike but suspect it is as stated above. More informed CABER's may be able to identify the manufacturer by looking at the frame.