Yes, Depending on where the DWI Conviction Occurred

Yes, depending on the county in which you received the original DWAI conviction. You may be able to take advantage of a motion process that permits the old conviction to be re-opened and substituted with a conviction for an alternative, less harmful charge.

Re-opening cases is very fact specific.  You should contact an attorney in your area and make an inquiry as to a possible coram nobis motion.