Do electrons become more likely to be found in certain places as the temperature approaches 0K?
Free electrons? Electrons in solids?
I was asking for a clarification of which system you are thinking about.
If they are completely free there is no reason for them to be in some particular place - their location will just depend on where you put them and their velocities.
If you have bound electrons in some potential, at 0 K in general they are more likely to be closer to a minimum of the potential.
Separate names with a comma.