Sharraxaadda

I have been on numerous sites with conflicting responses. I am hoping on this forum can help.

My community has both private and public streets. Further the HOA maintains only the private streets, but not the public ones (ex. De-icing streets, re-paving, etc)

Recently the HOA has decided to enforce no parking on the streets. However this is only for the homeowners and not visitors (even though visitors could potentially stay longer than a day)

My question is can they legally do so on Public streets maintained by the city?