All three versions are fine in correct English:
What color hat do you have?
What color is your hat?
What is the color of your hat?
(plus the variation in spelling "color" versus "colour" : both are correct)
"What color/colour hat do you have" is the closest translation to the Finnish version.
It seems there is some regional or personal preference with this type of construction. To me, what color hat do you have sounds absolutely natural. It's probably what I'd say myself. From comments here and comments regarding a similar sentence (linked below) and a discussion I found elsewhere online, it seems some English-speakers find this sentence entirely natural like me, and other English-speakers think it sounds unnatural. My suggestion would be to leave it as it is but allow the other responses too. (The variety of English they are using in this course seems to be very close to mine; when others object to some of their English usage, it generally has sounded okay to me, just as it does in this case.)
A similar discussion in this course, with "what color shirt": https://forum.duolingo.com/comment/39917286
A similar discussion regarding "what color hat" on another forum: https://forum.wordreference.com/threads/what-colour-of-hat-iphone.1161251/
It's not the same. Your examples don't leave room for more colors or more hats. When you ask: 'what color hat do you have?' you may be surprised to hear that they, in fact, have two hats.
I'd say that in your questions the focus is more on the color and in the one that was offered as a translation the focus is more on the posession of the hat.
"What color hat" is.
It sounds like you are thinking of it as "what" + "color hat" but it's actually "What color" + "hat" and it is correct.
Similarly you could ask "what color shirt do you have?", "what color jacket do you have" and so on. The question is "what color?" and then you add the noun after it.