It would need to be a very dense foam, equal to say 50 psi for me ( I like the rough ride)
The foam probably would get quite hot from the tire and retain it, I bet this avenue has been researched by the foam/chemical companies.
The flexible air-less wheel they designed some years ago would be a better direction to follow and more suitable to the 21'st century then my foam fill idea..
My Stepfather uses a white powder(I think it's powdered lead) in his 4x4 lawn tractors wheels for traction.
What kind of foam is in your friends tractors tires ?