Basement entrance: closed or open?

Hello everyone,

I have taken the step and bought a house from the year 1970. Now some work needs to be done. I want to have a new staircase installed. Next to the staircase is also the access to the basement. Currently, the basement is accessible through a door.
If it is relevant, my basement is not built underground, but level with the ground. So the basement floor is level with the street, for example. The house does not have modern insulation/sealing etc. just 1970 style.

I was at the stair builder today and he suggested installing an open staircase.

Does anyone have experience with that? Can you advise me on something or give tips?

Regards
amikx

Are the cellar rooms normally heated and also living spaces? Or only storage?

Would definitely close it. Otherwise, cold air will always rise from below, unless it is of course just as warm at the bottom as at the top, which I doubt.

The basement has a radiator and are not living spaces. Laundry rooms, etc. are in the basement