Can a cold cause nausea and dizziness?

Yes, it can: Many things can cause nausea and dizziness, including viral infections.

Yes: Viral upper respiratory infection can cause eustachian tube dysfunction, acute labyrinthitis, resulting in vertigo, dizziness, disequilibrium, post nasal drip, and activation of Vagus nerve, which leads to nausea.

Yes,: those types of symptoms are possible with viral illnesses.