How big can a nose cone be when in use with a rocket?

There's no absolute maximum. In terms of model rockets, the only critical requirement is that it physically fits; in models like the old Estes X-Ray the nose was significantly larger in diameter than the body tube; a balsa adapter and a short mylar tube was used to mate the large nose with the smaller body tube. A large nose actually helps stabilize the rocket by moving the center of mass forward.

The only other thing to consider is that the larger the nose, the larger the mass (assuming it's constructed of the same material). This means that a given engine will not produce as great an acceleration, so your rocket will not go as high or as far as it would with a smaller nose.