So, we decided to build him a cat house for him to hang out in and give him some shelter. With the weather we had this year, this was one of the better projects we built.
Step 1: Building box
Our cat house ended up 18" by 26" by 18" tall. Any size would do according to your cat's preference. We used exterior plywood left over from other projects and sealed the wood with waterproof paint. The roof/lid was attached with hinges to allow us to clean the inside. A strip of weather stripping around the lid helped seal out drafts. We had some plastic left over from a storm window repair, so added a small window to give some natural light.
A piece of leftover carpet (which can be easily removed for washing) added comfort A cat blanket from the local dollar store added some extra warmth and gives it that homey feeling.