Japanese · Pronunciation Guide
fu-yu, two beats — the "fu" uses both lips, not teeth on lip, and neither vowel is rounded.
fuyu
Two beats of matching size. Standard speech gives the word a rising contour with the drop landing on a following particle, so the melody resolves outside the word — but both morae inside it stay exactly the same length.
Listen: 冬
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冬はとても寒いです。
Fuyu wa totemo samui desu.
In winter it's very cold.
Listen: 冬はとても寒いです。
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冬はとても寒いです ends with 寒い (sa-mu-i), which contains a third unrounded u and a bare final i. So the sentence asks you to keep the lips flat three times in a short line, and to keep the mu and i of 寒い as separate beats.
"FOO-yoo" is wrong three times over: an English f made with teeth on lip, and two rounded vowels. Take the teeth out of it entirely, spread the lips, and keep both beats short. The bilabial ふ is one of the most reliable markers of a learner's accent.