Tony, This time of year is when I get started trapping. So, I have many years of cold weather canine trapping experience. What I do is obviously not the only way, but What I have learned from many years of cold weather trapping. You can't completely eliminate traps from freezing. Once it gets cold and STAYS that way you can. But a rain and freeze, or afternoon thaws and freeze can be tough. I can keep traps working in just about all conditions but the hard freeze after a rain. Nothing works with that situation, including peat, coveralls, or Calcium.

I use Calcium Chloride and VERY dry dirt from under barns or any other dry, odorless dirt source. Another little trick is to use waxed paper directly under the trap, jaws, and spring levers. I use wax paper most of the time as a pan cover, so I already have it on hand. Its best to cut or tear a piece to the right size to go under your trap. Wad up the paper into a tight little ball to break up the wax so it doesn't crinkle and make noise. Then bed your trap on top of it. The wax acts as a mold release so to speak.

I use Calcium Chloride over regular salt (Sodium Chloride). Both are hydroscopic, and draw moisture from the ground and air. However, Calcium Chloride produces a lot more heat from the chemical reaction as it draws water, and has a lot lower freezing point. So, it keeps traps working better in the colder temps. I buy the flake CC (don't get the pellets) from feed stores. I also run it through the blender and pulverize it. That way it blends in the dirt a lot better.
It is cheap! Dad and I have been using a 50lb bag for 6 years or better, and still have almost a 1/2 bag left.
So, my sequence is this:
Dig trap bed and get it level and where you want it.
Sprinkle entire bed with a light coat of CC.
Put in wax paper.
Bed trap
Layer dirt inside and outside trap.
Another layer of CC.
Final sifted cover over trap.
Light layer of CC.
Light layer of sifted dirt to cover CC.

Don't be afraid to USE it. I sprinkle it a couple inches outside the jaw spread around the entire trap. The only downside is it does leave a dark spot where you sifted dirt over your trap. That is from the moisture. I've never notice refusals from it though.