The Answer
The downward side of the free falling skydiver will get more wet because a they will be falling at roughly 10 times as fast as the rain (over 50 m/s vs about 5 m/s respectively).
To answer this question we need to look at how fast skydivers fall, and how fast rain falls. If the skydiver is falling faster than the rain the downward-facing side of them will get wet. If they are falling slower, the upward-facing side will. If they can manage to fall at the same speed, perhaps they wouldn’t get wet at all.
How fast does a skydiver fall?
Skydiving typically involves two distinct parts – the free fall and the canopy descent.
A skydiver in free fall generally begins with a downward velocity of 0 m/s when they are on the airplane and they will accelerate downward until they reach terminal velocity.
A skydiver in the belly-to-earth position reaches a terminal velocity of about 195 km/hr (54 m/s or 121 mph).
Once the parachute is opened, the skydiver’s speed is greatly reduced.
Parachutes are designed to reduce your terminal velocity by about 90 percent so you hit the ground at a relatively low speed of maybe 5–6 meters per second (roughly 20 km/h or 12 mph)—ideally, so you can land on your feet and walk away unharmed.
How fast does rain fall?
The size of a raindrop can vary, but the average size is roughly 6mm.
The terminal velocity of a 6-millimeter raindrop was found to be approximately 10 m/s. This value has been found to vary between 9 m/s and 13 m/s…
So…
When a skydiver is in free fall, they are traveling downward at 54 m/s, while rain is traveling slower at around 10 m/s. This means the relative speed of the rain from the perspective of the person is ~44 m/s upward. The front of the skydiver will get wet almost 4 1/2 times faster than if they were lying stationary on the ground facing upward.
When the skydiver’s descent is slowed by their parachute they are traveling at roughly 5 m/s while the rain is still traveling at roughly 10 m/s. So that would mean the rain is traveling downward at a relative speed of about 5 m/s, half the normal speed.
But…
A skydiver with an open parachute is beneath that very parachute, so the rain would be falling on the parachute, and not the skydiver, so technically they wouldn’t be getting wet at all (except for any rain they might hit due to horizontal travel since modern parachutes generally don’t all straight down.
In conclusion
The downward-facing side of the skydiver will get very wet during the free fall, and it will get a little wetter if they travel horizontally while under the parachute. At no time, except maybe during transitions, will the upward side of the skydiver get wet to any significant degree.
According to the Arizona Skydiving Center, the rain will sting a skydiver’s face due to the high relative speed of the rain against them as they fall. Because of this skydiver’s may turn over and face their back to the rain as they fall, turning back over only when it’s time to open the chute.