This is a little lengthy but will be most welcome:

'Wishing all our constituents a happy Christmas and a safe and prosperous New Year'

Go raibh maith agaibh in advance

You might use something like the following, but do wait to see whether someone else spots any problems or comes up with any better suggestions:

Le dea-mhéin dár dtoghthóirí go léir:
Nollaig mhaith dhaoibh!
agus
Athbhliain faoi shéan 's faoi mhaise dhaoibh!

Wishing for all of our voters:
Happy Christmas to you all!
and a
Prosperous and happy New Year for you all!

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.