All great advice.
I'll emphasise the umbrella - its great, esp when there is a call of nature, some companies even make hiking umbrellas !
Tarps are great, but a good vestibule makes everything much easier.
My good tent has one at each end, so one can be used for gear storage, and the other for access and for cooking.
This adds to the overall weight, but no more so than adding an extra tarp. Being integrated it also stands up well in strong wind or snow, better than a tarp (IMO, but I'm sure others may disagree) !
Other things to bring are: something to read, a game to play, or notebook to write in.
A simple pack of cards or (6) dice to play Zilch are family favourite of mine.