Is the hutch out in the open yard? Or is it inside a shed of some kind? The trays are to catch the bunny raisins. They do not have to be filled with shavings except to hold the pee or stop odor. If you leave the tray out of the bottom hutch, it will just fall onto the ground if you are outside. If the hutches are inside a shed or building or garage, you can definitely use canvas over the sides at night and pull it up for several hours during the warmest part of the day. Also,stacking bales of straw around the sides and back of the hutches will also serve as insulation.
If the rabbit hutches are under a separate roof (inside a shed or garage) you can also use work lamps - the kind that look like shiny metal bowls with a light bulb in the middle. With all wire cages I put a 100 watt light bulb in them and set them on top of the cage top wire. You will have to hang them somehow. You can use a heat lamb bulb but you can also use a floodlight bulb which is less hot. You can't use a heat lamp if the hutches are outside though, and if you have an open pole barn you have to make sure that rain blown in doesn't hit the hot bulb which can make it explode..
I am not familiar about that type of cold since I was always more concerned with using misters to keep my rabbits from dying in the heat here in southern California. Definitely use the drywall pieces to keep their feet from freezing to the wires which have heard about in some severe climates. They sit on the drywall and stay off the wire but if they get poop on the drywall, you just shake it off. You can also use carpet squares, but the urine will soak into them. I have used carpet squares soaked in water in the summer to cool rabbits down in 110 degree temps.
I have also seen short lengths of PVC drain pipe put into the hutch and used as "burrows" for the rabbits to go in. I don't know much about it since I have never used them.