[TexasGunLover]

Not quite true. Private property, in some circumstances, can still count as “the public square” or a “public forum” for purposes of 1st Amendment law.

No, it can't. If it's private property, it's not public, despite being open to the "public".

[Boogieman]

“No, it can’t.”

It certainly can, because the courts have made several such rulings.