There have been several experimental 4 wheel drive karts as far as I know. Big issue IMO is the more moving parts the more drag and more power lost. Is it worth it? Other than that with the current dirt tracksvand prep/tire combos you don´t really need much more traction in most cases. Maybe for a beast like the JAWA or similar.
in the early 80's Jerry Inman from Miss. built a 4x4 dirt car. On a dry slick track he broke all the track records, but when it got tacky, no one was man enough to drive it ( days before power steering).