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I'm no expert, but probably when the parasites get bad (i.e spring through first cold snap).

My granddad user to raise 1-2 hogs for slaughter each year. He would ALLWAYS wait until after the 2nd. good cold snap before he did the deed. He said to wait until it got cold, the colder the better, as pork would spoil on the ground before you could cut it up if it was hot.

I harvest and eat hogs all year long.  Its just about if you can process them in a timely fashion.  The 1st thing I do after I kill one is quarter it and put it on ice(within 2-3 hours).  If there is no store close by I always have ice in my ice chest and I quarter it on a disposable tarp or drop cloth.(I always carry a few)

Several years ago my sons each got hogs on a hunting trip to southern Oklahoma.  We brought the meat home and ate it.  That hunt took place in late June. 

I think BK9954 is on the right track about getting the animal hung, bled, gutted, skinned, & in the cooler ASAP.  Like he said: 2-3 hours.