Hi Malina,
The question here is about the prepositions 'to' and 'into'.
'To' is used to talk about where something is in relation to a larger area around it.
'Into' is used to talk about the movement of something, usually with a verb that expresses movement.
Therefore, 'go/get out into nature' is the better sentence as you are expressing the action of moving into nature.
I hope that helps!
Greg