Dry creeks are one of my favorite places to hunt for logging relics (and relics in general). I am not sure what you are hunting for though. I live in the Ozarks and that areas that I hunt are in the woods that have a lot of seasonal creeks running through them. When in a new area, I will hunt the seasonal creek beds first. They are almost always dry when I hit them. If I start finding horseshoes (my first hand forged horseshoe came from a seasonal creek bed), axe heads, tobacco tins, etc. I figure I am close to an area that had a camp or at least a break/lunch area upstream. There are times that I will hit a stream bed and not find anything. Other times I find more modern stuff. When that happens, I start looking around and usually find a dump site within a couple hundred yards and the stuff has washed down over the years.
One thing that I have noticed is a lot of the finds are DEEP. I dug an oil can up that was over 18" down. Heavy rains and flooding moves the gravel and stuff I guess. The digging is a lot easier than hard, dirt though.
Hope this helps some.
Doug
As for equipment, I use my regular metal detector since I am hunting dry gravel mostly. If there is water there I do take care to keep my control box well away from the water. I hunt with the largest coil that I have and in all metal mode since I am looking for iron.