Ice, mostly water ice on cold LH2 (liquid hydrogen) and LOX (liquid oxygen) tank surfaces with temperatures being low enough to condense, liquefy and freeze solid atmospheric water vapor on contact. Both these propellants are cryogenic to increase their storage density.
As the main stage ignites during liftoff, they're mostly shaken off the launcher due to the vibration of the sonic shock (basically just like we intentionally trigger avalanches with a loud noise, usually with explosives, but this time main engine ignition expands surrounding air so fast it produces a sonic boom, emphasized as it reflects off the ground and blast deflectors), producing that mist that you observe. And some still clings onto the launcher and boils-off during ascent due to aerodynamic heating, with most of it usually gone by the time the launch vehicle reaches maximum dynamic pressure (max q), but you can still observe smaller pieces falling off during staging from the interstage space where ice can form due to trapped bled-off propellants (tho some launch vehicles use an open interstage / aft skirt to help purge those bled-off propellants during ascent and prevent their rapid expansion due to aerodynamic heating, e.g. Soyuz).
Note that the Saturn V first stage used RP-1 (essentially a rocket grade kerosene) as fuel and LOX as oxidizer, and other stages used LH2 and LOX. How much and where the launch vehicle is covered by this condensation ice depends on where on the launch vehicle these tanks are placed, temperature at which cryogenic propellants are stored (LH2 is usually much colder than LOX), tank insulation, ullage and interstage volume, even how much time the launch vehicle sat fueled on the launchpad prior to launch, paint, and of course weather.
Part of the mist could also be due to purging of bled off propellants with gaseous nitrogen just prior to ignition, as can be seen in this slow motion video of Saturn V launch, but most of it would be condensation ice falling off cryogenic surfaces (also seen in the video after main engine ignition):