Well, an old-timer winemaker I used to work with would say, “The most natural fining agent for any wine is time.” What he meant was that with time, solids fall out, proteins eventually coagulate and fall to the bottom of the aging vessel and tartrates reach an equilibrium so they aren’t in excess and big crystals will precipitate as well. The problem with this approach when referring to fresh whites and rosé wines is that with enough time for all these chemical reactions to occur, enough oxidation and aging might take place in the wine such that it would be well past the time that you would want to bottle it. Whites and rosé wines are typically bottled within 4–12 months of harvest and part of their verve, charm and freshness is lost with extended time in barrel, keg or carboy.
That all being said, the fining agent you choose will depend on your definition of “natural.” If you mean using naturally-occurring substances, then things like bentonite (a natural clay that pulls out proteins), potassium bitartrate seed crystals (help precipitate excess tartaric acid that might form crystals later in the bottle), egg whites (pulls out excess tannins) and even isinglass (a protein isolated from the swim bladders of fish), and carbon powder (can bleach color from oxidized wine) all qualify, as do many other things. It’s important to read up on the topic. Browse any supplier’s catalog and you’ll see what I mean. For a simple white fining, to get it “heat stable” (remove excess protein so it won’t form a haze) and “cold stable” (remove excess potential tartrate crystals) is a good simple two step process to employ.
However, if by “natural” you mean you “don’t want to add anything” then don’t. Sometimes lees stirring for a couple of months, about once every week, can impart mouthfeel, help move some of these “time” reactions along and can help a wine taste more finished. It’s all up to you!