I think this is like many discussions or ideas, if it works for you and you get good feedback or feel good about it, then do it, if you get negative feedback or feel it is a waste of money and time or worse, don't do it.
I know that is overly simple but it is how it shakes out.
We send an annual card, it is somewhat seasonal but doesn't speak to a particular holiday just to the fact that we appreciated their business, hope they are doing well and that we are always here for them. I personalize each card to what we did, who they are, some might be one sentence, others a short paragraph if warranted.
My grandparents ran a boarding kennel that was after the first year, referral only and raised their whole family on it. Each year multiple times a year folks sent them cards, I've received quite a few cards in our first two years and agree, getting a card is awesome!
However, I try to build in each customer who seems to want it, a relationship that shows them I not only care about the job I'm doing for them, but I do care about them as people. Not fictitious, I do and it is part of what I love about running my own shop!
Some folks we know don't care to be bothered, just hire you for the job and don't visit with you for more than the time it takes to pay you or hire you, but the bulk of my clients 99.9% love to talk about wildlife and their families and such and I love that!
Happy holidays!

Or bah humbug, whichever suits ya!
Justin