Snowman's extremities drip and drop off (6)
I believe the answer is:
snooze
'drop off' is the definition.
(I know that snooze is a more specific form of catch a wink)
'snowman's extremities drip' is the wordplay.
'extremities' suggests removing the centre.
'drip' becomes 'ooze' (I am not sure about this - if you are sure you should believe this answer much more).
'snowman' with its centre taken out is 'sn'.
'sn'+'ooze'='SNOOZE'
'and' is the link.
Can you help me to learn more?
(Other definitions for snooze that I've seen before include "Some sleeping" , "Forty winks" , "A brief nap" , "Take a brief light sleep" , "Catnap" .)