Most of the parasites hunters warn about are external, such as wolves. I do not know if that is the proper name but it is a maggot from a blow fly between the skin and meat. It can be seen by a lump on the skin with a .17 caliber or so hole. Also deer ticks, lice and skin fungusses are an issue.
As for internal parasites most of what we eat does have internal parasites year round. They generally live in the intestine, heart or lungs and do not live in the meat we eat. Cold weather can not kill them as the body heat keeps them alive. You will not see the guts move. It is just a natural occurrence and is not as bad as it sounds. Even in the dead of winter dear have worms in their sinus cavities. I saw a taxidermist puling them out with forceps. He called them bots and said they froze them and used for fishing.
I have always followed the first hard frost advice for hunting. As for jacks, can't help you bud, but I would imagine a slow cooking recipe would tender up the stringy tough meat of an old one, just like an old swamp rabbit.