I've frozen cooked mince pies for years and they always seem to be absolutely fine, not dry at all. I put them in an airtight container as soon as they've cooled down from the oven and then straight into the freezer.
I do serve mine cold though, so if you serve yours warm them maybe don't cook them through completely so that when you warm them up they finish off cooking and don't burn or dry out.
I make hers and always freeze them raw in the tin. Leave overnigth then bash them out and store in ziplock bag in freezer.
Take them out 30 mins, put them in buttered tin,then oven for a few more mins than normal. Eggwash or milk and sprinkle with sugar before they go in. Or no sugar and then dust w icing sugar when they are hot out.
I cooked and froze them one year and when I reheated them they did seem a bit dry so I always freeze raw now.
I have just cooked some I froze raw a few weeks ago. I greased the tins, stuck them in without defrosting at all, milk glazed them and put them in at 180 c for 23 mins. Cooled on wire rack and dusted liberally with icing sugar.
They are extremely good this year, if I do say so myself. I am goin to have to make many, many more tomorrow.