WowAce

What it says on the title.  Had a mod that did this for me but it was last updated in Mists and finally broke with 10.0.  Seems right up Postal's alley, I just never bothered posting this suggestion before because, well, the other addon was still working.  :-P

Link to said other addon: https://www.wowace.com/projects/mail-attachment-count

I have a working copy of Mail-attachment-count, I updated it for pre-DF. And was working yesterday ... haven't checked that today's patch has broken it or not. They don't allow comments to post an update on their page. Not sure where I can put up a link for others.

Edited

Yes it's still working :)

I made a fanupdate for it on curseforge if you want a working copy for DragonFlight 

 https://www.curseforge.com/wow/addons/mailattachmentcount-fanupdate

 I thought about this one for a bit and have decided against adding this feature.  The reasons are 1) it tends to clutter the mail line information provided by blizzard 2) It's a rather redundant feature as Postal already does this if you hover over the mail icon for any specific mail as long as you have the Express feature "Add multiple item mail tooltips" turned on 3) as detailed above there is another addon that provides this functionality.  I do appreciate the suggestion.