I would say in the early spring. When the snow is first gone and before green-up. All the bucks will have dropped by then, they won't be buried in snow and the thick understory isn't there to hide them either. Shouldn't be any rodent gnaw on them yet by then either.

Obviously you can go whenever and often as you like. If you have the time, it's great to be in the woods. If you only have a couple days to search, I'd wait until you have the best chance.

Are there going to be other people shed-hunting where you go? That would be the only reason I would give for getting out as early as possible. The obvious ones will be picked up already - think Easter egg hunt.