Depending on budget, you could place a rolled up towel at the bottom of the door, or a cute draft excluder. You can even DIY them with ideas on Pinterest. I've also seen curtains work well, especially in older, draughty houses.
Use a towel! Or a you can put up two damage-free command hooks up either side of the door that can hold a curtain rod and drape a rod-pocket 100% blackout curtain on it which you can draw aside during the day or move the curtain rod to a different set of hooks so it’s out of your way! Hope this helps!