Impossible to say
The "short" explanation
Hirogen hunters appear in 8 Voyager episodes, two of which are double features. In only three episodes we see hunters with paint (always on their helmets) and in one episode a hunter performs the ritual of painting his helmet, without paint or helmet.
In the three episodes where helmets are painted, all three colours (white, red, green) appear on a helmet. A helmet is always painted with a single colour, always two stripes, but the stripes can appear both on the right side, both on the left side, or one stripe on either side: \\, //, \ /. Stripes start near the temple and end near the bridge of the nose. The times when we see the application, they are painted in that way (top to bottom).
Not all hunters have paint on their helmets, not even Alphas always have paint on their helmets. Paint does not signify rank (Alpha, Beta) because a double white stripe on the left is seen on both an Alpha and a Beta. Other Alphas are seen with red and green stripes on either side.
This is not enough information to draw any conclusion.
The full story
Message in a Bottle: A helmeted Hirogen is shown, no paint present.
Hunters: At the start of the hunt (for Tuvok and Seven of Nine), three colours of paint are shown: white, red and green. Two white stripes are applied on the left, with the right index finger (two swipes). The hunter is later shown to be right-handed. Later, this hunter states he wants to "claim the rights of a chief" (suggesting he is the Alpha) and claims his prey as trophies. Five colours of paint are shown: white, red, green, yellow and blue. He applies a single horizontal stripe of blue paint over the right eyebrow of both Tuvok and Seven of Nine. He then states: "These two must be the only relics.", indicating he has marked them for killing and extraction of their skeletons.
Prey: At the start of the hunt (for Species 8472) the same three colours of paint are shown: white, red and green. Again, two white stripes are applied on the left, but this time with the left index finger (two swipes). However, this hunter is later shown to be right-handed. He is also the Beta, as later the Alpha is shown with a red stripe on either side. When later on reinforcements arrive, the Alpha on the lead ship is shown with a green stripe on either side.
The Killing Game: Only two Hirogen are ever shown wearing a helmet. Neither one has paint on it.
Infinite Regress: During a mind-meld between Tuvok and Seven of Nine an unhelmeted Hirogen is shown briefly, an assimilation victim of Seven of Nine.
Tsunkatse: At the start of each Tsunkatse battle the Hirogen performs the helmet-painting ritual. He applies two stripes on the right side, with his left index and middle fingers (one swipe).
Unimatrix Zero, Part II: An unhelmeted Hirogen is shown briefly in Unimatrix Zero.
Flesh and Blood: An Alpha is shown with red stripes on either side, his Beta has white stripes on either side. Several dead Hirogen are shown without paint on their helmets. Hunting Hirogen are shown without paint on their helmets.
Hunter: The paint on the helmet designates some kind of proficiency as a hunter. Alphas are shown with a double white stripe left and with red stripes on either side. Twice we see an Alpha/Beta hunter duo where the Alpha has red stripes (on either side) and the Beta white stripes (once both on the left, the other time on either side).
Green paint is also shown on an Alpha, commanding the lead ship of a hunting party. This suggests a higher rank, most likely due to being a better hunter. So green > red > white.
Prey: Paint designates the worthiness of the prey. Both Tuvok and Seven of Nine are deemed unworthy after being caught. Perhaps yellow and blue are reserved for sub-par prey. The other colours could mean prey that was a match for a Hirogen hunter with the same colour paint.