You can please some of the people ALL of the time BUT not ALL of the people ALL of the time! Sound familiar? Get used to it in a HOA!
Your options are: 1. Have a special assessment to pay for the approved design and cost of the new mailboxes. You will need to know the cost of the mailboxes and installation costs. Don't forget you will need supplies such as concrete, posts, and someone to dig the holes!
2. If the HOA has the money for the job already, then approve and do the work.
3. Have the owner's replace the mailboxes at their own convenience but ONLY to the new mailbox design. That may not be the best. The mailbox design could go out of production or have owner's never replace.
Our HOA doesn't have mailboxes. We have a Mailbox house at the entrance of the HOA. Each person has a key to their box. This allows more parking options on the streets since there are no mailboxes to block. This is also where we have a central announcement board to post HOA information. The mailboxes are from the Post office and someone built a nice little "house" around it. We've had theft issues and the locks are easily replaced by the owners. The locks are around $5 and the mailman will install them for free if they need changed out.
This may be an option you may look into. Having a central mailbox instead of individual boxes.