primary purpose of varnish over exposy is UV protection.  so no UV no need for varnish.  Since if does change the colour slightly you might want to match it all up.  I did on my last built (floor baords on a SOF), in retrospect, I think I will skip that next time, just added weight and cost.

You want to varnish all sides to keep moisture from entering one side only and warping the wood.

 Check out the book "Understanding Wood" by Hoadley.

Lyle's advice would be good if under the seats was unsealed by epoxy.  That being said, I think it probably would be a good idea to varnish under the seats of the pram. Since the pram is an open boat with no decking, there might some possibility of the sun reaching in at an oblique angle and at least a couple of coats of varnish on the under side of the seats would be some protection.  I would definitely fully varnish the floor under the seats as there is a much higher chance of the sun hitting there.