Is there any advantage to setting the trap deep in the box other than it may make the set more snow proof?

In my mind a trap at the entrance may catch a hesitant mink who does not want to enter but will step on the coni pan to get a better look.

Put a 1 2/2 infront also for that curious coon fox fisher that comes along also. Hay I even have caught a few coyotes that way......jk

Trap depth and opening size increases the selectivity of animals that will be caught.

Can't say if a mink would shy away, I'm no mink trapper.

I have preferred setting out front at the mouth of the box or pocket set hole. If worried about snow accumulation I am sure you could use some ground material, flat rocks, sticks etc to give an over hang porch canopy effect in designing your boxes to help with the snow some if needed. I have used small pieces of plastic and aluminum coil stock, shingle pieces etc for protection if I feel it will help.

I make mink boxes with a 4-5 inch ovah hang ….and the rear of the box is a see through tight holed wire.And the entrance has a plywood plate with a 2 1/2 inch hole cut in it. Targets mink and weasel only

Yes, it provides for a consistant humane neck/thorax catch when set within 4-5 inches of the bait at back of the box. When the trap is set too far away from the bait the animal sometimes moves through the wire trigger or jumps over the pan and fires the trap with its body or hind feet, resulting in a hip catch. With a 120-trap set within 4-5 inches of the bait, you will get a neck or neck and thorax quick kill zone strike virtually every time. This occurs because the animal is stable at the bait, not moving through, and centered towards the trap when it is triggered.

Do you have any luck with boxes Coon Duke?

I tried them half heartedly one winter but found they wouldn't go in mine.

Baited Mink boxes are a great way to catch skunks and possems around here,

Nor could I get a mink in one. Not saying you guys wont.

Before the last BG rule change I was starting to get good with them for coon.
Was using a long box with 160 in each end, until a warden advised me that this was not legal. I thanked him for not letting me get ticketed, and just used one trap. Then started using foldable cages, then came the set back, recessed law.

The BG regs are tricky.