Can a non violent felon own and use firearms and carry them in their vehicles and use them to hunt in the state of Wyoming

No. Felons cannot possess firearms.

That is not entirely correct. It depends on where you live and the type of felony. Can a Felon Own a Gun? 5 Federal Law Loopholes (http://www.newsmax.com/FastFeatures/can-a-felon-own/2014/11/17/id/607940/)

It also depends on the type of gun. In some states a felon can use and possess a black powder gun.

It also depends on the type of gun. In some states a felon can use and possess a black powder gun.

One must look at federal law (See Ballenger's post) and state law. Either or both may prohibit firearm possession by a convicted felon.

Wyoming-6-8-102.� Use or possession of firearm by person convicted of certain felony offenses; penalties.

Any person who has previously pleaded guilty to or been convicted of committing or attempting to commit a violent felony or a felony under W.S. 6-5-204(b), and has not been pardoned and who uses or knowingly possesses any firearm is guilty of a felony punishable by imprisonment for not more than three (3) years, a fine of not more than five thousand dollars ($5,000.00), or both.
Need to look that up to see what constitutes this part of the law.
Black Powder arms are not covered under the Brady Law but are considered "weapons" in most states.

6-8-102.� Use or possession of firearm by person convicted of certain felony offenses; penalties.

Any person who has previously pleaded guilty to or been convicted of committing or attempting to commit a violent felony or a felony under W.S. 6-5-204(b), and has not been pardoned and who uses or knowingly possesses any firearm is guilty of a felony punishable by imprisonment for not more than three (3) years, a fine of not more than five thousand dollars ($5,000.00), or both.


Ref:
Wyoming Gun Laws | WyomingGunOwners.org (http://wyominggunowners.org/wyoming-gun-laws/)

...
Black Powder arms are not covered under the Brady Law but are considered "weapons" in most states.

The "Brady Bill" and the Gun Control Act are two different pieces of federal legislation. The former deals with reporting of sales, while the latter (see the link in ballengerb1's post) deals with possession by felons. The federal law prohibits possession by felons of "firearms" (which by definition excludes "antique firearms" designed or made in or before 1898). Most black powder rifles, even if designed and made today, would be OK under federal law, but as noted may be prohibited to felons in a particular state.

"18 U.S. Code § 921 - Definitions

(a) As used in this chapter— ...
(3) The term “firearm” means (A) any weapon (including a starter gun) which will or is designed to or may readily be converted to expel a projectile by the action of an explosive; (B) the frame or receiver of any such weapon; (C) any firearm muffler or firearm silencer; or (D) any destructive device. Such term does not include an antique firearm.
...
16) The term “antique firearm” means— (A) any firearm (including any firearm with a matchlock, flintlock, percussion cap, or similar type of ignition system) manufactured in or before 1898; or

(B) any replica of any firearm described in subparagraph (A) if such replica— (i) is not designed or redesigned for using rimfire or conventional centerfire fixed ammunition, or

(ii) uses rimfire or conventional centerfire fixed ammunition which is no longer manufactured in the United States and which is not readily available in the ordinary channels of commercial trade; or

(C) any muzzle loading rifle, muzzle loading shotgun, or muzzle loading pistol, which is designed to use black powder, or a black powder substitute, and which cannot use fixed ammunition."

Cdad's post includes a link to the Wyoming statute. That statute proves that:

"As used in this section:...
(ii)� “Firearm” means any pistol, revolver or derringer, designed to be fired by the use of a single hand."

Note that the definition (as is the federal definition) is oddly under-inclusive. As I read it, in Wyoming the term means only a handgun. So possession of any long gun by a felon would be ok by Wyoming State law, although (as explained above) a violation of federal law unless it is an "antique firearm" as defined. The laws don't conflict and state law is not preempted: one could (depending on circumstances) be convicted of violation of the federal law, the state law, or both.