Well, strictly speaking no they do not but a few years ago I discovered watermixable oil paints. Interestingly they contain no water, rather like traditional oil paints they are made with linseed oil or safflower oil but have been modified so that they will mix and clean up with water. The delicious buttery texture, rich colour and long drying times associated with traditional oils are still there, but brushes and palettes are SO much easier to clean and they are better for your health and for the environment. There is no need for hazardous solvents such as turpentine which is fantastic especially if, like me, you paint at home and since Covid this is increasingly the norm for many!
In the past I have dallied with acrylics but for a number of years now I have preferred oils because I like how the buttery paint can be added, removed and pushed around on the canvas whilst it is still wet and workable. I find them very responsive. I have found acrylics frustrating at times because they can dry very quickly although this is obviously the appeal for many artists! If you are at the exciting start of your painting journey I would suggest you let yourself play and try EVERYTHING! Watercolour, acrylic, oil, gouache, ink to name but a few. If you have a look at any good art supply website you will be spoilt for choice and there are wonderfully tempting new products being introduced all the time. I would definitely suggest you give watermixable oils a go too, they get a big thumbs up from me!