Rich, Not all dogwoods have opposite leaves.
Cornus alternifolia,(Pagoda dogwood) has alternate leaves as its name specifies. I believe that all the other dogwoods have opposite leaves. Red Osier is a shrub type dogwood like Rich said. There are tree and shrub types and all are suitable for making arrows if the shoots are long enough and of good diameter.
David, pics of the plants will help to ID what you have found. Leaves(not out yet) will be a better help with IDing them. Most dogwood leaves are similar but the actual flowers(not the bracts around the flowers) will give you a better ID of dogwood...and other plants.There are many shoots out there that will make arrows. I cut some willow not long ago to give it a try. I have noticed that its diameter will be bigger than most of the other shoots I have used and the shafts will be a bit lighter. If serviceable arrows can be made from horse weed, dog fennel and goldenrod then practically any wood shoots will make serviceable arrows. Pat