Frosty, alternately bitchy (3)
I believe the answer is:
icy
'frosty' is the definition.
('icy' can be a synonym of 'frosty')
'alternately bitchy' is the wordplay.
'alternately' indicates alternate letters.
The alternating letters of 'bitchy' are 'ICY'.
(Other definitions for icy that I've seen before include "Frosty, arctic" , "Frosty and slippy" , "(Of relations) very hostile" , "Glacial" , "Very cold, hostile" .)