What kind of charges am I facing?

It is a crime to fail to appear for criminal charges so you could be charged with that offense. In addition, you still have to face the initial DWI charge. if the warrant is effective you would deal with both offenses and, if found guilty, would be sentenced based upon the convictions and the law at the time you failed to appear.

I am not licensed in new Hampshire, so out of respect for any experienced DUI attorney who answers this question, I would direct you to that answer first. However, my answer is you face a bench warrant (and thus possible bail setting) as well as a second-time DUI. I would definitely hire an attorney who may be able to have the DUI dismissed based on a lack of a speedy trial (your Sixth Amendment right). I see this scenario quite often in CA and the speedy trial defense can work - and does.

You should speak to a NH criminal defense attorney as soon as possible. The question noted above does not contain a lot of details, so it is difficult to determine your course of action. Specifically, the time that has elapsed since your missed appearance is not noted, and the actual outcome from the DWI from 10 years ago is not detailed. Generally, courts in NH will issue a bench warrant for failing to appear. If you follow up on the missed appearance timely, your or your attorney can sometimes get a new date scheduled and the arrest warrant removed. It helps if you have a good reason for not appearing. the impact on your prior DWI is difficult to determine from your question. There is a statutory scheme in NH that addresses multiple offenses. Depending upon when you missed your most recent appearance, the court could issue a default, and then you would have two convictions against you and you could face arrest for the warrant for failure to appear, as well as an arrest for driving without a license.