I am very interested in this. I have always just used a Drop D but I like this idea much better. Did it take an adjustment period to get used to this tuning?
Also, what type of strings are you using and what is being used by some of the studio guys?
What type of basses as well?
It didn't take me very long to get used to it personally, although I did have to be more mindful of not plucking too hard initially (which forced me to develop a lighter touch, which is beneficial in itself). When I started using downtuning, it was with the idea that I would use whatever tuning sounded best for each individual bass, i.e. one bass might be a half step down, another might be a whole, yet another in C#, etc... But that got a little confusing and I really found that I just liked D standard best anyway. It strengthens the fundamental and takes away some of the upper harmonic "bouncyness" without getting unplayably loose (I tried going as far as C standard, which didn't work for me personally).
Although I started downtuning mostly for tone reasons, it has proven to be convenient to for a lot of the music I play, which does tend to have a lot of drop-D and whatnot. And even though I mostly play five string, 95% of the time, the 5th string is a thumbrest. The feel is another big point for me - the bass feels really resonant and vibratory when it's tuned lower, I think.
As far as my gear, I use a Lakland Darryl Jones 5, Peavey t-40 & MIM Fender P-bass w/Fralins, all with medium Elixirs or La Bella flats. As I said above, I like the feeling of wide vibrations from the strings, so I don't use larger, tighter string gauges. I've got really no idea what the studio guys use, you'll have to ask them
Another thing: some of the other guys in this thread (nathan thomas and masmasbasso, particularly) have made good points about the image of the 4-string in a country band, particularly in Nashville. While I've never personally gotten flack or been made fun of for playing a 5-string bass, image does matter because it reflects your mindset. And for better or worse, the 4-string is a image/mindset statement that I think works in your favor in a country setting, and in fact I'm mostly playing 4-string these days. So if you need lower than standard notes, and in a lot of newer country you will, downtuning works out well.
I was jammin' out to some Taylor Swift (Love Story and Fearless come to mind) and this tuning just made sense to me! Sure, it was a bit of a mental workout at first. But once I got into the swing of it, it felt great. And as an added bonus, the reduced tension made my bass play like buttah, of which it has not been known to do. 
