How about scenting your arrows with a trappers scent of choice then training your Beagle to find them. Just kidding, but it could work if you were committed to training the dog I suppose.
Worth trying your yarn idea, keep varying the length, thickness and attachment method until you found acceptable arrow flight…or not. Kind of like a fish arrow, it should work. No harm in trying. As little as 6” could help find arrows perhaps.
Like lpcjon2, I use the brightest fletch I have, use judos and follow the arrow hole in the snow and start making perpendicular passes with a stick. It's not fun, I agree!
Kris