Yes, they can find them by nose under the snow or grass. Josie really excels at finding arrows lost under grass, field decoy stakes forgotten in a ploughed field, empty hulls, you name it.
The reason Sunny is carrying the arrow back by the fletching is because that's all that was sticking out of the tumbleweed. It was lodged pretty solidly in the dirt after passing through the dreaded bush, so she tugged it out by the back of the arrow. She usually holds it in the middle, as they are taught to do with birds.
They deliver the arrow to hand, the same as with birds...