Is Earth's "Stone Age" believable?

I am currently working on a world in which humans evolved in a world with a relatively short winter season, and are thus able to use stone tools.<br><br>My problem lies with the transition between the "Paleo" era, in which humans had no clothing, to the "Mesolithic" era, in which they do. The Paleo humans were able to adapt to the changing climate, and found ways to protect themselves from the cold, and thus made the transition to the Mesolithic.<br><br>However, the Mesolithic humans, who already had clothing, did not find these adaptations sufficient to protect them from the cold, and thus began to migrate to warmer regions, where they were able to live in harmony with their environment.<br><br>Is this believable? Or would it be more believable for the Mesolithic humans to have developed more complex clothing and shelter? Or should they not even have developed clothing?<br><br>I'm really interested in feedback on this, as I want my story to be believable and engaging.<br><br>TL;DR: Is it believable for humans to go from wearing no clothing to wearing animal fur?<br><br>&#x200B;