Seasonal Affective Disorder, is not, however: https://en.wikipedia.org/wiki/Seasonal_affective_disorder

A quick Google search does seem to confirm this and at reputable sources such as Psychology Today and the Mayo Clinic. However that should not be a reason to dismiss increased awareness especially as an outreach to those experiencing depression and suicidal thoughts. In other words, it's always a good time to talk about it and to try to help. If the holidays increase awareness and get people talking about it I don't see that as a bad thing even if there isn't a statistical increase in suicide.

Edit: typo and formatting

It really doesn't matter if it's a myth if you feel like that. The pressures that you can feel when depressed and surrounded by family create bad situations that might result in an attempt later, once everyone is gone, or simply a really sad holiday. Frankly, neither of these is an acceptable outcome. This is the 21st century and a human being shouldn't need to feel scared and alone anymore.

Yes it is:

http://www.snopes.com/holidays/christmas/suicide.asp

Snopes suggest it falls slightly over the holiday from 34 per million people to 30 per million people and then rises to 41 per million people at New Year’s.

I've noticed a lot of people feeling rather dysphoric lately. Myself, I always feel very strange around mid Oct-mid Dec, I think due to the change in seasons and my natural cycle of brain chemistry (which isn't ideal). I'm not concerned about the holidays in particular, but when you do have a drab family or social life, it's hard not to feel confronted by that at Christmas and the New Year.

The economic situation as affected many people negatively, especially trying at a time that one hopes to have extra money for their family. I'd believe that we have more than an average share of despondence these days.

As detailed in:

http://www.snopes.com/holidays/christmas/suicide.asp

It might be a myth but it still happens and it still hurts - I lost someone on the 28th of December 2009.