Assuming you can't walk through walls, you can only cross through a given door one time, and you have to cross through a door to "visit" it, this is impossible. Because...
Rooms 1, 2, and 4 have odd numbers of doors. Logically, if a room has an odd number of doors with our rules, if you start outside the room, you must end inside the room. Similarly, if you start inside the room, you must end outside of it. Draw some lines and you'll see what I mean -- no matter what, for each time you enter a room, you must leave it unless you are ending in that room.
Here's an image demonstrating this (left - start in, end out; right - start out, end in)
Because there are three different rooms that have odd numbers of doors, no matter where you start you logically need to end in multiple rooms to be able to solve the puzzle, making it impossible.