Christmas trees, being pines, are monoecious, meaning that they have both "male" and "female" parts on the same tree. They're actually a terrible choice for a story which pulls the "mothers are strong" trope, since they're a "single gender" species. So then, why do these Christmas trees make a big deal about gender? They're not really Christmas trees. They're an alien species that resembles Christmas trees.
Alternately, the trees wanted a female carrier because their concept of The Ark is a pine cone, i.e. the female part of a coniferous tree. A woman who'd borne children was simply the closest mammalian equivalent of a seed-bearing cone.
Possibly he was worried he might fall out of the hammock if he woke up and couldn't see where he was.
Crossing over with Fridge Horror, the forest is consistently referred to as being made of Androzani trees. As in "The Caves of Androzani". As in the planets Androzani Major and Minor, which in that serial were engaged in a rather brutal war. In fact, it's implied that the forest is on Androzani Minor. And yet the Doctor describes the planet with the forest as "This is one of the safest planets I know! There's never any danger here . . ." (Yes, that ends up not being the case.) Excuse me?