On all terrain tires what depth do you need to replace the tire for offroad use

I have the stock wrangler territory. I'm going to replace them but I can't get them until mid Jan. I leave on an overlanding trip in Utah in a week. Just class 3 trails. My tires are between 7 and 8 32nds

 

If the trails you are going on can be done with normal AT tires then I would not worry about it until maybe 4/32. Obviously if your doing large mud pits you have to crawl out of then you want plenty of tread but I would consider tires at 7/32nds to be almost new.