Is it possible to have a magnetic "vehicle" without induction?

I say vehicle, but I’ don’t care if it’s small. Flea sized is okay.
Can magnetism in a small self contained vehicle make it move horizontal to the ground? Or water. Could be a floating thing in a lab sink.
And by self contained I mean not having power input from the outside but could have batteries or fuel and equipment onboard.

A natural magnet suspended by a balloon will rotate to point north/south, but its center of gravity won’t move.

And I guess that if you had a battery, coil, etc. on that balloon, with a remote control (or trained flea to start it) that you could create an electromagnet that would attract or repel the earth and the balloon would rise or sink.

Can you make something move horizontally along or across magnetic lines? Or would the forces cancel and it would sit there mocking you and your avinaut flea?

If I understand your question I don’t see why not. Plenty of motors use magnetic forces to produce motion, and there are such things as linear motors.

Would a magnetohydrodynamic drive count?

Seems to me if you have a natural magnet up with a balloon, it will head to the nearest magnetic poll with no motor. Magnets attract and the earth is a magnet. Maybe we should warn Canada we’re sending magnets through their airspace.

Ah! That reminds me; I understand that in orbit it’s possible to raise and lower your altitude by running electricity through a cable and basically hoisting yourself with the earth’s magnetic field. I understand that theoretically if you had a big and light enough superconductor ring at the North or South Pole you could levitate right off the planet into space.