Do I have to switch my license?

As long as you are just a student.............you are not required to do anything.  Just keep everything as is.

As long as you do not work and are just a student and you still claim that your legal residence is New Hampshire, you do not need to change your driver's license or car license / registration, or even your car insurance, but it might be be cheaper and easier, espcially when it comes to renewing car registration. If I rtemember right from living there, New Hampshire requires an annual car safety inspection in order to renew the registration. Unless you are planning to drive the car back to NH when the inspection needs to be renewewd, that's a problem. Besides that, Arizona insurance covers cracked windshields without having to pay the insurance deductible, and I guarantee you will get a cracked windshield if you stay long enough. If you get a job or you want to claim arizona residence at somen point, you'll need to change both. 

Because you used the magic word "move", yes.

If you MOVE to a state, then you have to change your license and registration.

If you merely VISIT the state, and do not MOVE there, then you keep the license and registration from your home state and do not have to change it.

I was stopped at a DWI checkpoint in AZ.  I had a NY license and had been in AZ for 7 months.  I was advised that I needed to get an AZ license BECAUSE I was here more than 6 months AND I was using my AZ address was my residence address.

Maybe, and that's final.  This question gets asked a lot, because most people don't understand how a home address works.  Lemmy break it down for you.

Legally, you can only have one home address (officially called your address for legal service).  Also legally, that home address better be the same on all your ID cards and official documents.  You don't want to play the Address Game, which is played by having (just for example) this address for your taxes and employment stuff and this other address for your licence, and this other-other address for your insurance, and so on and so forth.  The Address Game, while really popular, is a game nobody ever wins.

If you say your home address is in Arizona, it is.  If you say your home address is in NH and you're just visiting Arizona, it is.  You and you alone decide where you live and where you're visiting, and there is no time limit for either.  Your driver's licence, insurance, plates / registration, employment / tax info, and all your official documentation should all be sent to your home address, no exceptions.  Since you get to decide where that address is, and since you can only have one legal address at a time, it's just a matter of figuring out where you want that address to be.  

Why is it so important to have the same address on all your official stuff, you ask?  Because having multiple legal home addresses is a common game played by fraud artists, mob bosses, wanted fugitives, international terrorists and other model citizens.  And trust me, you don't want to even be suspected of being any of those, not even a little bit.

if you maintain a permanent residence in NH, you do not have to switch.  "Permanent" usually means you get mail there.

No.  You do not have to switch your license.  Full time college students attending school out of state have special rules.

However, you must notify your insurance company that you will be going to school in Az.

Most of the answers here completely missed the fact that you will be a college student.  Here is a quotation from the AZ.  DMV website:

 "Out-of-state students enrolled with seven or more semester hours, are not considered Arizona residents, regardless of employment."

Almost every state in the union has very similar rules for college students.

Are you going back to New Hampshire after college?  Are you going to go back to New Hampshire to vote for Kamala for President in '24?  If you are going to Arizona *just* for school, still consider you to be a New Hampshire resident, then you keep your New Hampshire driver's license.

If you want to stay in Arizona, keep living in Arizona, living with the rabid red-necks, suffer the 120 degree summer heat, then you need to change your residence and get a Arizona driver's license.

Insurance companies want to know where you will be driving.  Has nothing about legal residence.

Go to the Arizona DMV website and check.