Consensus says Nov 15 -25 for a 10 day diy whitetail hunt in North Idaho. Also about 10% or so of the deer are mulies which takes a different tag. Check with your hunting regulation lawyer.
Also the pheasant hunting can be a good as anywhere in the lower Clearwater, however since a hard winter in January 2017 the weather has been too cold and wet during nesting the end of May with poor hatches since. Didn't hunt north last season, in Nov 2020 very few pheasants. Chased them a few days between deer hunts and jumped a couple but didn't pull the trigger. Quail and huns can be around but their numbers are low too. Chukars were numerous in one area and shot them. The steepest pheasant hunting anywhere, and very lightly hunted. Killed roosters in Doug fir - Ponderosa pines forest sometimes. Dry land wheat and big buck country. Like this pic., is in 11A which is nearly 100% private though. Pheasants are probably all on private ground, not impossible to get permission but probably going to get a lot on no's first. Because of so few bird hunters, easier to get permission for than to deer hunt.