Green’s Dictionary of Slang

1. ill-tempered [given wool n.¹ (2), ? link to keep one’s hair on v.].

1864, 1867, 1870		Hotten Sl. Dict.
1920		Advocate (Burnie, Tas.) 5 June 7/2: The beak got woolly last time, and threatened to put the boot in if he tried that lurk again.

2. tipsy, a little drunk.

1932		J. Dixon Free To Love 145: One’s my limit [...] Got to think of the job. If I’m woolly, they might fire me.
1955		H. Ainley In Order to Die 169: We finished that bottle in the same manner as the first—she had half and Hartz and I shared the other, but whereas he and I were definitely woolly, she hadn’t turned a hair .