When it comes to giving tips the first true test is if you have the money. In all honesty when going someplace when a tip is expected you should figure it in the costs so you know you have enough. With something like this though if you can’t give then you can’t give and a thank you card will suffice. A thank you card is great no matter the circumstances.
My second thought is how often do you see your hairdresser? If it is on a regular basis and they do good work then I would say your hairdresser does deserve a holiday tip even if you don’t see them in December. There are still holidays in January and in November so missing Christmas doesn’t exempt you from the obligation. Anyhow, as I see it, it is more of a “year well done” gift than a “merry christmas” gift. This of course only applies if you do have the money to give a tip.