Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Yes, painting nature is permissible. However, to make pictures, paintings or to have any such item which resembles a living being is prohibited in Islam.
A person came to Ibn 'Abbas (RadhuyAllahu Anhuma) and said: I am the person who paints pictures; give me a religious verdict about them. He (Ibn 'Abbas) said to him: Come near me (still further). He came near him so much so that he placed his hand upon his head and said: I am going to narrate to you what I heard from Allah's Messenger (Sallallahu Alaihi Wasallam). I heard him say: All the painters who make pictures would be in the fire of Hell. The soul will be breathed in every picture prepared by him and it shall punish him in the Hell, and he (Ibn 'Abbas) said: If you have to do it at all, then paint the pictures of trees and lifeless things. (Muslim)
Therefore, even giving such things to non-Muslims is not permissible.