Maybe wrong, but that looks like a Birch seedling to me.
Careful about pruning Hydrangea, it is very easy to remove the flower buds for next year. They are not normally pruned except to remove any dead or dying branches.
We are in the process of regenerating ours by removing about a 1/3 of the oldest branches at the base. That way there are plenty of flowers while the new growth matures enough to flower. Now is as good a time as any. Normal pruning just involves removing the spent flower head back to the bud which is just behind it.

could be but my first thought was one of the maples/sycamore with not very cut leaves.
either way it is a tree seedling and I would remove it.

as for hydrangea I agree with owdboggy. The spent flowers protect next yrs buds from frost.

I thought Grey Poplar but only a guess.

I always wait until early Spring to prune hydrangea because the older shoots will protect the now ones over the frosty weather (if we have any!) Then its more or less just removing last year's dead flowers