Got an Answer?
"Hey *other mothers name* this is *your name*. I was wondering if you and *their child* would like to join us for a playdate on such and such a day at such and such a place? Cheers 🙂"
Why would you not do exactly the same thing? Seems fairly casual (non obligatory) wording to me.
Just write your name (Johnnys mum) and number and write a comment that says call me if you would like a play date over the holidays. If the kids are old enough don’t even write a comment. Tell the kid to get mum to call me for a play date on the holidays