I am on supervised probation for a misdemeanor in NC. Can I still go hunting?

Check with your PO and Game commission.

Doesn't sound very promising if the info below is accurate and up-to-date. It appears that it is illegal for a person on probation of any kind to possess a gun of any type in N.C.
Don't know about crossbows, etc.

"Illegal Possession of a Handgun or Long Gun

It is illegal for certain people to possess a handgun or long gun, including, but not limited to:

Convicted felon (who has not applied for a restoration of his gun rights under North Carolina law) (See more about felonies and firearms)
Undocumented or Illegal Aliens
Fugitives from Justice
Abuser of alcohol, or user of illegal controlled substances
People convicted of Domestic Violence offenses (See more here about DV laws and guns)
People discharged from military service under dishonorable conditions
Someone who has an active 50B that alleges violence or a domestic threat (See here about DVPO and 50B orders and guns)
Someone who has an active court order that bars gun possession
Someone who is on probation of any kind (See more about probation and firearms *) "

* asterisk added by me : The referred to "see more about...." includes the following:

"Submit to warrantless searches by a law enforcement officer of the defendant's person and of the defendant's vehicle, upon a reasonable suspicion that the defendant is engaged in criminal activity or is in possession of a firearm, explosive device, or other deadly weapon listed in N.C.G.S. 14-269 without written permission of the court. "

All of the above from: Probation following a NC DWI Conviction | Aggressive Raleigh Criminal Attorney

I have no way to verify or disprove the above information.

Edit: I did not note the reference to DWI convictions until I saw it come up in the link here. If you have probation for another type conviction, you will have to dig deeper to determine the regulation for that type probation.

It appears that the answer depends on how OP proposes to "go hunting". Although Federal law, as well as state law, apparently, prohibits convicted felons from possessing modern firearms, I gather that OP is not a convicted felon. But, from Smearcase's post, it also appears that state law in NC also prohibits misdemeanor probationers from possessing firearms. But it says nothing about other weapons for hunting.

Also, one might check the definition of "handgun or long gun". If state law is like Federal law, certain obsolete firearms are not considered "firearms".

AK,
You are correct. Conviction on a felony is a whole different ballgame.

Also, when I first read that "Someone who is on probation of any kind (See more about probation and firearms *) " clause I did not realize that it was still under the heading of DWI probation.

PanteraGuy needs to provide more detail about his conviction.