Most "cozy room" advice is really "buy more furniture" advice, which is not much use if you rent, or the room is small, or you just do not want more stuff. The good news is that the things that actually make a room feel warm are cheap, small and mostly about light.
1. Change the light before you change anything else
A single bright ceiling light flattens a room and makes it feel like an office. The fix is two or three low, warm light sources instead: a lamp on the floor, something glowing on a shelf, a warm bulb by the bed. The sunset projection lamp throws a wide amber disc across a wall and does a lot of this work on its own. A candle warmer lamp gives you a small pool of warm light and a scent at the same time. Turn the big light off and see how different the room feels before you spend anything else.
2. Add exactly one soft texture
Rooms feel cold when every surface is hard. You do not need a full soft-furnishing overhaul: one textured corduroy cushion on a chair or the end of the bed, or swapping your pillowcase for silk or linen, changes how the whole room reads. Pick a neutral tone so it works with what you already own.
3. Give the room a smell
Scent is the fastest shortcut to "this is a place I relax." A flame diffuser or a backflow incense burner both do it, and both give you something quietly moving to look at while they work. Keep it low and consistent rather than strong.
4. Clear one surface
Free, and it matters. Pick the surface you see first when you walk in and take everything off it that does not need to be there. A room with one calm, clear surface reads as looked-after even if the rest is a bit chaotic.
5. Do it in the evening
Cozy is a night-time quality. Try all of this at 9pm with the curtains closed, not at noon. If the room feels good then, it is done. There is a full version of this as a routine in the 20-minute bedroom reset.
Everything mentioned here is under $60 and ships free to 40 countries, and 15% comes off automatically on orders over $35. The light and scent edit is the place to start.