First, it is a good idea, whenever posible, to store the kart indoors, like a garage or storage building, on a wooden floor where available. This will help prevent moisture from attacking the metal parts and causing excessive rust. There is no way to prevent all moisture, but this will help. If inside storage is not an option, cover the kart to protect it from direct rainfall.

Next, the fuel system must be drained or otherwise cared for. I put Sta-Bil gasoline stabilizer in a gallon of gas and run the engine for several minutes to get the mixture into the carburetor. Then I drain the gas tank and run the remainder of gasoline out of the system. This can take a while, but gasoline is only good for a short time, then it starts to form a varnish that can damage the inside of the engine and make it run poorly, or not at all. Gasoline stabilizer extends the life of gasoline, but when left in the tank could make your gas illegal for racing.
If using methanol your system has probably already been drained after the last race, but if it hasn't then disconnect the fuel line and run the methanol out of the line. Then replace the methanol with gasoline, and run the gasoline into the engine. Remove the line from the gas and run that out of the engine until the engine quits.

Last on my list is tire preparation. Tires are effected by UV radiation and ozone. Tires are designed with protection for these, but when sitting dormant for several months the built in protection is not effective. UV radiation will be prevented by indoor storage or covering the kart, which I've already recommended. Ozone can be reduced by indoor storage, or some people like to rap their tires with plastic rap. Check the tires from time to time as this may also damage the tires in rare circumstances. Some remove the tires and store them inside the house. Another way is to use a tire protectorate, but not the normal tire sprays available in your average retail store, as these are actually worse than doing nothing at all. Get a product such as 303 Aerospace Protectant or other non-petroleum based product. This covers the tire sidewalls without damaging the tires natural protection. Check with your track's technical inspector or sanctioning body to make sure this is not considered an illegal tire prep first. Now, put the chassis up on blocks to get the tires off of the ground and reduce the air pressure.

Preparing the engine: (coming soon)

You should now be ready for winter. It's up to you to decide how to spend your Saturday nights until next race season.