Freezing milk or cream will usually cause it to separate upon thawing, so if you add it to your coffee, you will get a "curdled" look. This does not affect the taste, but it looks a little weird. I freeze individual coffee creamer cups all the time, since my youngest loves to "eat" them right out of the freezer. I've thrown them in my coffee occasionally, and it's still all right, you can just see tiny white particles floating in the liquid. (That's the milk fat)
Freezing the flavoured creamers would probably have the same result, but if you're mixing it into something else, like icing or cake batter, then the results shouldn't be any different than using fresh.
On that note, I sure hope the Creme Brulee Coffee Mate Creamer is still available when I visit NY this week - I plan to stock up! It's soooo good, and I used up what I bought last time so quickly in my coffee and iced cappucino, that none made it into any of my cakes or icings! And of course, it's not available in Canada....
