Both are correct in English. Many nouns regularly serve as adjectives in English and they're called attributive nouns. (like wool scarf, cotton clothing, tree farms etc.) ^.^
It would be great if it accepted "woolly coat" too, as that's probably more common in the UK than "wool" or "woollen" in this context.
"Woolen" isn't a term that you're going to hear much in the United States. We tend to take the material and use it as an adjective almost in the same way the Germans create compound words. Wood is the only material that I can think of that transforms into "wooden" with any consistency.
It said above, this is now accepted. Was it wrong in your answer? If so, report it...
woolen, just like golden, leaden, wooden, archaic silvern and leathern...
Jacket=Ζακέτα/Μπουφάν, but please also pay attention to the spelling of "woolen".
Whoops, it was actually included in our alternatives xD Thanks for the link.
NB. Correction - My phone even refuses to let me type "woolen" with the prevalent American spelling and insists on auto-correcting it to the prevalent Commonwealth spelling "woollen"...!