Under Minnesota law, a person can be arrested if a police officer has probable cause that a crime has been committed in their presence, and often when not in their presence as well. This is not true of a "petty misdemeanor" such as most speeding tickets.
I cannot recall any driving without a license -type offenses that are not a crime. The most common are Driving After Revocation/Suspension/Cancellation. These are all crimes, subject to arrest. The police officer has discretion not arrest, and to issue a citation - but one could not be sure about whether they would. In terms of sentencing if convicted, these crimes generally do not result in jail for a first offense, but do if there are prior similar offenses. In addition, the drivers license gets revoked again and longer every time there is a conviction for this type of crime.