"Please don't go to that mountain in the winter."
I feel like there should be a different particle after 冬. Maybe 冬に or 冬には according to google translate? 冬は doesn't feel right.
I feel that it could be では to say during the winter, but I'm not sure. I'm still learning grammar :/
I'm a native speaker. To me 冬に and 冬には would be a little strange because then に is being used twice to point to the same verb, making the intent ambiguous.
That being said, both 冬はその山に or その山は冬に are acceptable; as per usual, the main difference is connotation (is the topic the mountain or the winter?).
I am also a native speaker. For me, 冬は, 冬に and 冬には, all of them sounds natural, and they means the same.