I sealed off 2 vents in my basement when we moved in.
I do not notice a difference between the standing on the floor barefoot on the first floor vs second floor (when on the same type of surface).
My basement is partially unfinished, with minimal insulation below grade (maybe 3/4 rigid foam below grade and nothing on concrete above grade). It is cooler in the basement during the winter, but not terrible. In the 5 years we have been here we have not had it get anywhere close to freezing. I wouldn't consider actively heating this space until I have addressed the insualtion (concrete has basically NO r-value).
But passive heating . . . between having the heating system in the basement, the ducts for the first floor (uninsulated), a washer/dryer, and the food storage deep freezer there is enough heat to keep things from freezing up.
If I were you I would keep them closed so long as it doesn't risk freezing and any use of the basement remains comfortable (we have our home gym, laundry, food storage, and brewery in the basement).