Cotton clothes that are made from 100% cotton are considered biodegradable. This is due to cotton natural composition that will in time biodegrade leaving no harmful products in the environment. This being said, some clothing will have other compounds added to it that no longer make it fully eco friendly. T-shirts with certain prints on or certain types of colourings can poison the soil that they are being degraded in.
The short answer to the question is yes, however, multiple facets need to be taken into account. Although an item of clothes may be described as 100% cotton it may have accessories that are not biodegradable and that will not be able to be added to a compost heap. Below is a list of materials that are and are not biodegradable.
Natural Biodegradable fabrics:
The first step to understanding if the product will biodegrade will be ensuring that only the above natural fabrics are present in the making of the piece of clothing. If any of the non-biodegradable fabrics are present even at a low level, the piece will not be fully biodegradable and may take several hundred years to break down.
The second step is to understand the extras or accessories that may come with the piece of clothing that will not be mentioned in the label. These are things like buttons, zips, prints, and also the label itself.
If you are wanting to compost of your clothing yourself, you should always ensure that the piece of clothing you are composting only contains the natural fibers listed above and that you remove all of the non-biodegradable accessories before adding to the heap.
Cotton is a natural material and therefore will biodegrade naturally. It is also able to biodegrade with or without oxygen meaning it can degrade in standard landfills (most modern landfills are sealed to reduce oxygen) but will degrade more efficiently in a compost heap.