Is it rude to ask wedding guests to pay for parking? Details Inside.

My partner and I are planning a budget wedding and we are leaning towards holding it at a state park. The park charges a $5 parking fee per vehicle. Would it be rude to expect each vehicle to pay for this as they enter? Should we include a small note about it on the invitation so they can expect it? If we do need to pay for parking, how would we distribute the passes? (I kind of doubt we can buy them in advance enough to send with the invitations, but it’s possible.)

Thanks for your opinions.