How to Recreate the Old Classic Snake with Hinged Joints

You're biggest problem here is likely the MASS of the connected parts as you stitch them to the head. This is known as Forward and Inverse Kinematics if you want to look it up online.

In short, each new object you attach as "tail" has Mass, and is acting like an anchor to the head part of your Snake.

The easiest way to overcome this would be making dummy objects with zero size and zero mass as the joint holders for your new tail pieces. These need to be rigid bodies to work with the physics, and they'll have TINY impacts, but probably nothing that you'll see once their size is reduced to nothing and mass to zero. (even tho the manual recommends not setting mass to zero, I've tested in on some of the stuff I'm doing, and it works the way I want)

Then you'll need to attach "tail section" objects to these dummy objects, and ensure that these visible tail sections do not have rigidbodies on them.

Hope that works for you.

You try to use physics on a movement that's not based on physics. If the snake turns, the body(-parts) follow the exact path of the head. But in the "real" world if you form a rectangle with a rope and you pull on one end the rope will not stay on the path you've set up, at least not without some sheaves at the corners to keep the rope on track.

The old snake game doesn't even move the body parts. The head moves on and a new bodypart is created at the last head's position. The last part of the snakes tail is removed to simulate the movement.

What you want is a fix movement along fix waypoints (that are set at direction changes). I don't know what you want to use as snake body because the bodyparts have to bend around the corners.(skinned mesh?).

The real challange when creating a snake-clone in 3D is to create this "movement engine" to handle the movement correctly (not too sharp curves or it will look strange).

As I said: to use physics is not the right choice here.

It would be possible to use physics but you would have to create invisible colliders (cylinders) that act as sheaves at the corners. But that would restrict the movement and if the chain is really long the spring behaviour of the joints will cause problems.