There are animals such as pigs and elephants that wallow in mud which possibly serves as protection from sunburn. There are also some plants such as Aloe vera (Aloe vera) and Jewelweed (Impatiens capensis) which are believed to help soothe burns which may help after a sunburn has already occurred. Are there any natural materials that one could find and use in the wild to naturally protect against sunburn?
As you said yourself: mud. Or cotton as Gabriel answered, or wood, or leaves, or bark, or anything that stops light from reaching your skin. Is there any natural material that without any processing can be applied as a cream, is nearly invisible in the visible spectrum yet stops much of the UV-rays? Not to my knowledge. Which is why we have to make it. But most natural materials will block most of the UV-rays. This is also one of the main reasons why there is no natural sunblock. A tree is protected from UV light by its bark, it doesn't need to produce a near invisible cream that blocks UV-rays. And since most natural materials block much of the UV light they will protect you from sunburn and skin cancer. Often better than commercial sun cream, as you probably already know from wearing clothes. They just don't do it while letting most of the visible light hit your skin and while letting you look like you're not covered by anything.
The mucous from the marine animal mushroom coral, is a natural sunscreen, which is designed to keep the coral itself from burning in the sun. The mushroom coral is only found in coral reefs in certain parts of the world, so it might be hard to find in the wild. According to a historian, Bear Grylls is said to have used it to rub some mucous on himself and then put the coral back in the water.
There might be some validity to this, as outlined here: http://www.qm.qld.gov.au/microsites/biodiscovery/05human-impact/sunscreen-for-corals.html. It also describes the coral's ability to produce a substance to try to protect itself from the sun, although it doesn't specifically mention a way for people to use it.
Wood ash As @Monster said:
anything that stops light from reaching your skin.
The OP her/himself suggested mud. All you need to get wood ash is a campfire, which you probably want anyway, in the OP's scenario.
Survivopedia in 9 Survival Uses of Wood Ash says:
Natural Camouflage This is kind of a no-brainer but there may come a time when you just don’t want to be seen. You may be hunting or you may be waiting for human predators to invade your space. Whatever the reason, wood ash is a quick, natural camouflage.
On a similar note, sunburn can be lethal and if you don’t have any sunscreen, rub wood ash on your skin to block the sun’s rays. (emphasis added)
Of course, this isn't a silky cream, but wood ash is portable. You can easily carry several days worth, or more, unless you are hiking in short shorts and a sleeveless shirt. Obviously wood ash will be harder to obtain above timberline or in a desert, exactly the places where you need sunscreen the most. But even above timberline there are often scattered trees and scattered downed wood, and deserts may have some woody scrub. Wood ash is stickier than mud, particularly if it is deposited over a layer of campfire grime from a smoky campfire.
Caveats: (1) Make sure the wood ash is cold before applying it to your skin. (2) An anonymous editor made the point (which I have in turn edited) that fresh wood ash mixed with water is caustic, and should not be applied near your eyes, and may irritate your skin. Old wood ash will weather to a carbonate.
It depends on what level of processing makes you feel something is no longer natural.
Typical Sunscreens use Zinc Oxide as a UV blocking agent, as it is photo-stable and creates a nearly invisible layer (when using the highly-processed nanostructure form of the mineral). Zinc Oxide is naturally formed as both the mineral Wurtzite, and the mineral Zincblende. One or both of these 2 minerals could be powdered and rubbed onto the skin for a somewhat ineffective sunscreen. Alternatively, you could look up one of the hundreds of recipes for homemade lotion, and add the powdered mineral to it to make your own sunscreen. You won't get the same level of protection as commercial sunscreen, but you will avoid the under-researched effects of the aforementioned nanostructures.
To clarify, the reasons Zinc Oxide nanostructures are so common in commercial sunscreens are the FDA GRAS status (you can eat Zinc Oxide safely per FDA rating), and the lack of pigmentation that non-nanostructured Zinc Oxide would leave on the skin after rubbing in the sunscreen (goes on white, rubs in clear type of thing).
Red Ochre is a natural earth pigment found in clays that are rich in iron. It's been used for thousands of years by cultures around the world as a natural sunblock. It's also the same pigment used in ancient cave paintings. Native American Indians "war paint" was often worn as a sunblock, and was made out of ochres. Being a clay makes it easier to prepare it into an applicable paste, but it's essentially mud on your face.
Most white substances are usually good. As a bush assumption you can assume that reflectance in visible range means reflectance in UV range. You can grind rock against rock and mix with spit or water. The active components of sunblock are usually pretty common minerals. Rutile, Zinc oxides etc. The organic ones have a tendency to be banned for toxicity after a few years after introduction...
A quick Google search reveals that carrot seed oil has an SPF of 40 and raspberry seed oil has an SPF of 30. The reliability of the site is not established.
Just FYI here's a formal study of herbal sunscreens. One of the products tested claimed to be carrot seed based but another person evaluated the ingredients and discovered zinc oxide which probably contributed largely to the SPF.
The white dust, technically "bloom", found on the trunks of aspen (Populus tremuloides) trees has been used as a sun block. Some trees have more than others. Rubbing a hand on the bark and transferring the dust to your skin does noticeably leave a whitened area so I'm inclined to believe it is some help. There are numerous species of Populus, so it might be possible to find other trees with similar benefit.