Do you have a photo?
Is it just a bronzing? Are the leaves still supple? Could just be a little winter color. I don't have nigra but I have other conifers that will bronze up now.

I'm not certain how to determine if it is bronzing but it could be? Sorry I don't have a pic. The leaves are still supple on each of the trees. Some trees have thinned out since planting but the leaves are supple.

Your description sounds like bronzing to me. The easiest solution is if you can get someone to post a pic for you if you can't do it yourself. Or you can email it to me and I will do it. Many here can tell you at a glance if it is just the normal winter color.
Otherwise, you might ask your source, at least alerting them to a possible problem so you may act on your warranty.

OK I have the photos - sorry took so long.

Pic 1 - The leaves of the tree - all look this way
http://i144.photobucket.com/albums/r198/cabezon_bucket/DSC_0582.jpg

Pic 2 - The contrast from front of tree and back being sheltered from wind by the fence
http://i144.photobucket.com/albums/r198/cabezon_bucket/DSC_0583.jpg

Pic3 - Two of the trees - one of left has thinned since planting
http://i144.photobucket.com/albums/r198/cabezon_bucket/DSC_0585.jpg

Hope this helps! Thank you for all responses to date.

I will post the pics for you.

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Here are two links that mention the yellow brown color this shrub might develop from winterburn and that is what the first two photos look like to me. I hope others will give their opinion. Also, go to the shrub forum and you can link them to this post.
The third had quite a bit of leaf drop. When did it thin out? Before or after the cold weather? Are they exposed to alot of wind? You could try to protect them from the wind with burlap this season and maybe next while they get established though that sounds like a lot of trouble, doesn't it. They may bounce back once spring comes but you should give your nursery a heads up. I'm sure 20 6' arborvitea was a small investment.
http://hcs.osu.edu/pocketgardener/source/description/th_talis.html

Here is a link that might be useful: Note mention of yellow brown winterburn

Thank you for your response loretta. The third thinned during late summer into Fall. They are exposed to some wind. All of the trees look the same way so I am hoping it may be wind burn and the tree will green in the spring again. I did drive by a nursery this weekend which had some arbor planted in mass and looked somewhat similar to what I am seeing so that gives me hope too.

Another question - when planting a tree of this size, I was told by the landscaper to leave the burlap on and not to remove it or open it. Would anyone advise differently?

On the roots? I am wondering if you will find anyone here that would advise that. The twine is cut and the burlap pulled back. In my Master Gardener classes, it is taught as a big mistake. Here is a link to the PDF file from Rutgers Extension that says just that and it is the answer you will get if you call your extension center.

Here is another site with a compilation of answers on that question put out by another trustworthy source - Utah State University. If your landscaper left the roots wrapped, he did you wrong.

Here is a link that might be useful: Transplanting Trees and Shrubs

That looks to me like some bronzing, but also some dying. Yeah, you gotta loosen the burlap at planting; that could be the problem. But I'd also like to know what the watering schedule and method was after planting, and what sorts of fertilizers and pesticides, if any, were applied to the trees and/or the lawn.

(I found that my arbs are not particularly fond of stuff added to the soil, except a mild shot of miracle gro in spring and early fall, but only after having been well established.)

That said, I'm no arb expert. I lost four of mine in the last year.

Cabezon, Just wondering... did your arbs ever make it? Did they grow new foliage? Please let us know! I am in the same boat right now, and don't know what (if anything) to do. :( Thanks!

I have heard from old timers not to buy large shrubs or trees---to get them smaller. Because when they take them from the soil, a lot of roots get left behind. This is in adiditon to the normal transplant shock any plant will have, and then the transplanted shrub/tree has to contend with maybe a dry summer, a windy winter, etc.

I have been told, and I have also observed, that if you buy the plant smaller/younger, and more of its root system is intact, that it will grow faster & "catch up to" the bigger ones, which struggle having been transplanted after losing many of their roots.