'Fuzzy' hats, also known as "long hairs", "velvours" and "kitten finish hats" were quite popular during the Golden Era, particularly during the 'teens, '20s and into the '30s. They even soldiered on through to the 1950s, though the form and style had changed significantly.
Check out these two scans from a 1922 Mont. Ward catalog (click photos to enlarge):
Notice that the crowns were very tall, over 5" while the brims remained medium to narrow width. This was fairly common during this period and into the 1930s.
The Turgis fedora below is from the late 1920s or early 1930s. Note that is has the same tall crown (5") and narrow brim (2 1/8") as the hats pictured above. The fuzziness of this hat is on the long end of the fur length spectrum, thus making it very soft and fluffy. The fur of this hat could easily be combed.
Long haired hats are made a little differently from regular fedoras. While the fur used in regular fedoras is cut short and densely compacted, the fur used in long hair fedoras is cut longer and allowed to stand up, making for the fluffy appearance and soft feel.
Next is a 1940s Royal Stetson long hair with a rather crazy ribbon. Note that this hat falls into the medium area of hair length on the fuzziness spectrum: not as long as the Turgis above but still fairly long.
Interestingly this hat is meant for warmer weather, as the lack of a liner and the company tag attached to the inside top of the crown indicates:
Last but not least, this 1950s Stevens hat is on the very short end of the fuzziness spectrum. It is still a very soft fur hat and fuzzier than regular fedoras of the time but not as soft or fuzzy as either of the two previous hats.
As a side note, Adolf Hitler favored very long haired hats similar to the Turgis pictured above. That being said, long haired hats were a very popular style in Germany during the 1930s, especially in the Bavarian region so to associate the fuzzy fedora primarily with Hitler would be a great disservice to millinery history.
And while the fuzzy fedora is thankfully not usually associated with Hitler, the 1970s turned it into something for pimps and gansters.
What a shame.