when does hunting finish

Depends on where you are in the country, but usually around March.

Our hunt's closing meet is the last weekend of Feb due to lambing, but some hunts are lucky to continue into April.
 
Very generally:

In a grass livestock country anytime from mid February to early March (including much of Ireland)

In an agricultural country mid to late March

In a moorland / heath / woodland country into April

Some hunts used to pack up after killing a May fox - pre ban of course
 
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