Is it worth it to visit England in December?
Yes, of course, it's only marginally more miserable than normal.*
If it is, what major attractions would still be open or would be suited to winter travel?
All the great galleries, museums, cathedrals, castles, palaces and country houses will be open.
Even in summer there are few outdoor attractions to consider (except the odd garden), because the weather can be so unreliable.*
I am aware that the days are short and scenery will not look as nice as in the summer, but is does it still look good?
Some of us are no longer in the spring of our lives, yet we still "look good". England fits this description.*
*From an Aussie, these comments are deliberately intended to rile our Pommy friends.