Framing
You need to be careful in the application of wood. What do you intend to make out of the wood? Low gage steel tubing should be used as the main go kart frame components for all the major "stress" points- the heaviest load carrying members. Especially off road, you will need the flexural strength and durability of the steel for rough/bumpy conditions. Wood is no where near as good in tension or compression as steel. Technically, the strength of a structural member depends on alot of nerdy equations relating to area moment of inertia, resistance to bending and shear ("modulus"), and load concentrations. But suffice it to say, stick with tubing. How much do the riders weigh? If you are building the cart for a small rider or child, you might think about converting a hand truck (dolly). The tubing is quite strong, and provides a good basic frame shape to start with. It even has wheels you can use. Further, if you cut off the nose extension, that can be made into a motor mounting plate and mounts for a decent set of pillow blocks (axle bearings). An industrial hand truck will cost anywhere from $40-$60, and you will get the wheels, tube frame, and axle. Not bad!!
As far as welding, check with a local high school shop class or community college that offers fabrication and welding. Probably for a small fee, or for 'class credit', maybe they can make a class project out of your go kart frame.