This is a tricky area.  The [US Constitution][1] forbids the federal government (refered to as the state) from infringing on the rights of its citizens.  The states then each have their own governing document, most of which incorporate the restrictions to include the state government.  There is a point of [controversy][2] among some as to wether or not those restrictions are automatically conferred upon any governments underneath them.

Here is a copy of the [ordinance in question][3]. (Thank you Oddthinking)  

Under the [Arkanasas Constitution][4] I would expect that the Article 1 Section 4 may provide some protection to the group:

> 4. Right of assembly and of petition. The right of the people
> peaceably to assemble, to consult for the common good; and to
> petition, by address or remonstrance, the government, or any
> department thereof, shall never be abridged.


Article 12 (Starts page 40) deals with the powers of local governments and businesses incorporated in the state of Arkansas.

Section 4:
> 4. Limitation on legislative and taxing power - Local bond issues. No
> municipal corporation shall be authorized to pass any laws contrary to
> the general laws of the state;

(There is more to it on the site that does not seem relavent)

However Arkansas does allow [limited home rule][5] which I would assume was used to enact this law.  I would expect that the state constitution protections above would protect from this should it ever get to court.



  [1]: http://archives.gov/exhibits/charters/constitution_transcript.html
  [2]: http://en.wikipedia.org/wiki/Arkansas_Constitution#Controversy
  [3]: http://www.arktimes.com/images/blogimages/2011/07/13/1310568750-gouldordinance.pdf
  [4]: http://www.arkleg.state.ar.us/assembly/Summary/ArkansasConstitution1874.pdf
  [5]: http://en.wikipedia.org/wiki/Home_rule_in_america