I think you are looking at this a bit backwards. You're asking whether or not the position is likely to remain open or closed and want to use that to direct your plans. The game is yours to make. You should instead be looking at your position (and your own strengths as a player) and let that guide you on whether an open or closed position would be in your favor. If it doesn't seem feasible for you to exploit the benefits of an open position, try to keep it closed. If it doesn't seem feasible to exploit the benefits of a closed position, open it up.
I think people oftentimes think about open/closed positions as a way to determine whether or not certain actions are advisable (e.g. trading a knight or attacking a king). But you could also look at it the other way. Look at the ways the strategies differ for open and closed positions and judge which one is more feasible to work with based on what you have going so far. Once you know that, figure out what you need to do to reach an open or closed position. Then, once you've achieved that goal, work on exploiting the strengths that led you to pursue this position.
The key thing to remember is that the game isn't something that just happens. You are making choices on what to do. It's not so much a question of whether or not the position will be open or closed, it's a question of which position should you be working towards.
However, that is more towards your question about "if it will still be [open or closed] in the future?" For that, you should decide which is preferable and try to find strategies to move the game to whichever state you want.
As for how to determine if a position is open or closed, it all comes down to the pawns. If several pawns have been exchanged and there are few pawns in the center, it is open. If most of the pawns are still present on the board, and the center pawns in particular are blocked and not able to be exchanged, it is closed. You can open up a position by exchanging pawns, and you can close a position by blocking pawns.