There is another aspect of this issue to consider. When someone invites you onto their private property, they also invite some of your rights to come along with you. Otherwise, they would be perfectly within their rights to put video cameras in the ladies' restroom in violation of their female employee's right to a certain amount or privacy, etc. Do you see where I'm going with this?
So, I believe this is far more complicated that a simple matter of the employer's property rights and the resolution of it will rely on how well the employer conveyed their rules to the employees (did they sign an agreement not to bring weapons onto company property?) and where the state law stands on the right to carry a weapon in your car?
That is actually quite legal, so long as you inform your employees of the practice.