It does indeed! Pheasants and deer are only property while confined so that they cannot escape, so it is possible to steal deer from a park or deer farm but not from the wild, where it is the lesser offence of poaching.
Once deer are dead and have been ‘reduced into possession’ they become ‘property’ and belong to the landowner or the holder of the shooting rights.
Thus, although the surface of the road is the responsibility of some Authority or other, the land itself still belongs to the landowner on either side.
A dead deer is therefore his property and removing it without permission could constitute theft.