[s2e7] Hair Today, Gone Tomorrow Link

While Shaun the Sheep fits your specific S2E7 tag, several other series have used this exact title for their own hair-related storylines: Hair Today, Gone Tomorrow | Shaun the Sheep Wiki | Fandom

In this 7-minute episode, which first aired on December 1, 2009, on BBC One: [S2E7] Hair Today, Gone Tomorrow

While the Farmer is distracted, Shaun "borrows" the wig to show off to the flock. Chaos ensues when a bird snatches the wig away, leading to a frantic chase. While Shaun the Sheep fits your specific S2E7

Shaun and Bitzer must work together to retrieve and return the hairpiece before the Farmer leaves for his date. The Origin of the Title which first aired on December 1