In space, there is no such thing as up and down. If by "in space" you mean "when weightless" then you have no gravity to define what is up and what is down so everything feels the same. As soon as you accelerate (either speed up, slow down or change direction) then you feel the force of that acceleration. You may experience "up" as the direction opposite the direction of that force.

There are a couple of sci-fi stories (Robert Heinlein, Arthur C Clarke ?) which imagine the lack of orientation caused by zero gravity. For example, man in EVA spacewalk (with magnetic handholds) on apparently horizontal surface, suddenly perceiving it as vertical and self as head-down, causing panic.

Sci-fi spaceships are usually rotated to provide pseudo-gravity internally, as well as to even out solar heating. If you are on the outside, then everywhere is down as soon as you move off the axis of rotation.

Much to my shame, I was once so drunk as to be discoverd flat on my back on a lawn under a starry sky, with my fingers dug inches into the ground, absolutely convinced I was about to fall into the endless depths of space.

I think it would be no problem to make a 180 degree turn around the horizontal axis of your body, so that your head and feet change places, if you have something to hold on to. I'm doubtful about doing so in free space without anything, though. To turn your back to where the front was would be much easier using your arms, you can try it standing on your knees on an office chair. Even so, with no friction to soften the movement it would be hard do stop turning just in time.