We a are still getting 107 degree days where I live. If your winters are that cool reversing the fan so it sucks in the outside air will work far better than trying to suck out the hot air from the tent. You may need to regulate it so it doesn't get too cold. Like using a Y connector, and a butterfly valve on the side that runs to the window. The other end of the Y connector would run outside the tent but inside the window. Unless the tent is air tight this will cool down the room somewhat.
During the summer, if the room the tent is located in has a central heating and ac vent and your parents don't mind, you may be able to utilize that source for the cool air. The
lights give off heat and there is nothing that you can do to change that unless you get different lights, so that heat needs to go somewhere. If you can use the AC for cool air during the summer then you can vent the exhaust out the window, though I think that the lights would genorate much more heat than you can get rid of. You may need to still use a system like I described in the other post as well as insulate each bucket and the reservoir to achieve the right water temp.
Again, I know that you want to keep everything inside the tent. But if you could talk your parents into letting you keep the plants outside, you could use the free sunlight for light, and just keep the
nutrient holding tank inside the window. Then just run the feed and return lines through the window. You would need to keep the plants above the window level so gravity will bring the
nutrients back inside the window, otherwise you would need another
pump for that. You will still need to do something to cool the nutrients down but you wont be heating up the room the tent is in and wasting all that AC, as well as saving all that electricity the lights and fans would be using. (NOTE: you will need to insulate the buckets the plants are in to help keep the root zone cool. If the nutrient solution is cool the root zone will be cool.)