I have a light on my ceiling, rather than being a socket with a bulb it is a ring of small LEDs with a plastic diffusing cover over top. I would love to play with the lighting, making it warner, or possibly deep blue, but I am not sure where to start - I'm wondering whether this is a generic light cover that I can replace with a tinted one or if such things are not standardized. (https://i.stack.imgur.com/iVqdV.jpg)
You could try to change the color character of the LED light a small amount using an alternate diffuser cover or by adding color filter sheets as mentioned in comments by @jsotola but I would comment that the results are not going to be optimum. Color filters work by allowing only certain ranges of wavelengths of light to pass through while others are rejected or attenuated by a large amount. With an LED light source, which are not broad spectrum devices, the resultant light level through the filter will likely not be particularly useful as a light source.
My suggestion would be to consider changing the character of that LED light fixture by adding additional color selected light to either the fixture or the room by installing an RGB LED light strip. These strips can be controlled to emit a huge selection of different colors that would increase the net light output into the room instead of reducing it.
You would have to install a separate power source and wiring for the RGB LED strip and it's color controller. If you try to do something inside the existing fixture you may have issues with safety where added low voltage circuitry is installed next to AC mains voltages so do consider the options very carefully before starting to experiment with these ideas.