I was a hunter years before I was a hiker and have read some really good points here.
Wear lots of blaze orange. An orange hat is as important as an orange vest. You can get vests from the outdoors section of KMart or WallyMart. They range from thin, almost weighless nylon vests, to more heavier, insulated ones.
Never wear white. Too much like a deer's tail or throat.
I'd avoid bright blue during the turkey season. Its very close to a male turkey's head color, especially in the Spring turkey season.
Consider getting a dog collar with a loud bell. Some of the bird hunting sites sell them. Bird hunters collar their dogs with them so they know where the dog is in thick cover and know they are "on point" when the bell is silent. Those bells carry a long way in the quiet of the woods and will alert a hunter to your presence as well as your 4 footed companion.
Be very careful even bringing your dog in the woods where there are lots of deer hunters. In many states, it is a illegal for a dog to run a deer, and it is not unknown for hunters to shoot dogs they suspect are chasing a deer. Personally, I wouldn't take a chance that a guy with a firearm might see my dog running across his deer stand and make an incorrect assumption.
Most hunters who are sitting, use their sense of hearing to first listen for deer. They will assume that the slow, steady walking noise they hear is another human. The sound of a running dog is much more like a large, running animal and the flash of a dog running by could cause a tragic mistake by a careless hunter.
Consider being especially careful in the very early morning hours or just before dark. Those are the times that deer are most active and hunters are aware of that. Orange, at that time of the day, can be unrecognizable. I think it has to do with something called "red shift" that makes red shades appear black. Your four legged friend, moving thru the woods may not have the benefit of his orange vest showing up well early and late in the day. In some cases, hunters eek-out the last minutes of the day, when they can barely see. Be careful.
If you see vehicles at trailheads that look like hunters are around, or encounter hunters in the woods, make noise as you hike. Hum your favorite song, talk with your hiking partners, keep up a dialog with your dog. It lets the hunters know you're coming. I would avoid opening day of the firearms season in areas known to be frequented by hunters. You may spoil their day by moving around in the woods, and for those of you who are spooked by this sport, it may spoil your day as well.
Finally, during the deer season, consider avoiding trails with long or shallow approaches, or where you're in relatively flat terrain for long periods of time. Hunting clothes, equipment, ammo, and firearms weigh a lot. While some hunters will climb to get where the deer are, the vast majority prefer much flatter terrain. Trails that climb steeply from the trailhead will get you past the vast majority of hunters, and much more quickly.
Hope you don't mind all the advice.
PB