The construction is simple and only takes about 2 hours. Here's how to do it.

Materials needed:

bullet1 sheet 4' x 8' exterior grade plywood siding (Roughex is the brand I chose because it matched our house.)
bullet2 - 2"x2"x8' pieces of treated pine
bullet2 sheets 20" x 30" exterior 1/2" plywood
bullet1 30" x 6" piece of plywood for shelf
bullet1 sheet 24" x 36" exterior 1/2" plywood (for roof)
bulletScrap of rolled roofing paper cut to size
bulletInsulation - 1/2" foam board. I used available scraps to line interior walls.
bulletTube of liquid nails (to hold the insulation to the inside walls)
bullet1 ceramic screw-in light fixture (no switch)
bulletOutdoor grade 16-3 electrical wire, length as needed
bullet1 waterproof rubber cap (male electrical plug for the end of the cord)
bullet5-6 insulated wire staples (to fasten the wire to the roof)
bulletTwo hinges to suit.
bulletAssorted nails or screws for construction

Note: If you have not done electrical wiring before, then have someone who is familiar with it help you out, or hire an electrician. If you choose to do this project, you take all your own risks. I am only showing you what I did for our cats.

The construction is to first make the floor which is a double floor, 20"x30", with there being a dead air space between the two pieces. The spacer is a perimeter of 2x2's. Drill a 1/2" hole in the floor's bottom piece at each corner so any water can run out. The floor is longer than the box so there can be a porch.

Next, layout the sides, back and front on the sheet of siding and cut them however you can. I used a power saw, be safe!

Cut four corner braces of 2'"x2", the front ones being longer than the rear! The house I built is about 24" high at the front and 20" high at the back to allow for a slanted roof.

Begin assembly by attaching the sides to the outside edges of the floor. Do not mount them flush with the bottom edge -- they should be about 1 to 1-1/2" higher than the bottom edge. Install the rear in the same manner and attach the corner braces.

Measure the resulting opening in the front, and cut a piece of siding for the front. Also cut out an entry for the cats. There should be a cleat (2"x2" strip of wood) mounted on the inside of the floor's front to allow attaching the front to the floor.

Cut the insulation foam board to fit the interior walls. Attach using liquid nail.

Measure and fit the shelf; attach using 2 short cleats front and back. I attached mine to the side opposite the entrance hole. There's room enough for two adult cats and who knows how many kits

The roof should overhang equally sides and rear, with a longer dimension forming a roof for the "porch". Flip the whole unit over onto the roof to attach the hinges, it's easier! The top could actually be left uncovered if it's made of exterior grade or treated plywood, but it will last longer with some sort of covering, such as a remnant of rolled roofing (tar-paper)

If you must place this on the ground, I would recommend a few small bricks or concrete pavers/blocks to help keep it dry. A nice bed of stones will also work as long as it's higher than ground level. Position the shelter so that the front opening faces away from your cold prevailing wind directions.

As for any wiring, I'll leave that up to you. Painting is also an option, but the chosen wood will stand up to the elements just fine as-is. Place a nice not-too-thick padded cozy thing on the floor, and show it to the cats. Heck, maybe they've already been helping you with this, and know all about it! Others may be suspicious at first, but many will go right in to check it out. When it gets cold, there may be territorial squabbles over "who gets the house"!