We could see that Theon Greyjoy helped Sansa Stark escape from Winterfell which was under Ramsay's control by jumping off the wall. The outer wall is said to be about 80 feet high. How did both of them survive jumping from that height? It is highly unlikely to survive that jump even if there was snow.
Covered at this Physics.SE question: https://physics.stackexchange.com/questions/167077/freefall-into-snow
Yes: You can do it.
No: It won't kill you.
It does however depend on factors such as how much snow there is, is it powder or compacted, whether the landing is steep or flat. Falls of 100 feet or more are noted in comments.
TL;DR: Characters survive their falls from heights due to plot armour.
Looking back over the scene it isn't clear at all how they actually survive the jump. The snow at the bottom of the wall doesn't actually look that deep and you never see them land. The following image is of the look down the wall to the ground before they jump:
The snow also looks quite compact. The two could have injuries but ignore them due to adrenaline taking over. Here's the scene for reference:
Note that in the above scene Theon pushes Myranda from the wall that is less high and has no snow and she is killed on impact. Though she doesn't land feet first but on her side/back.
We next see them in Season 6 Episode 1 with them both still hurriedly running through the snow and it doesn't look much more than ankle deep at best.
Obviously they are further away from Winterfell so the snow won't be exactly the same but they're still hurrying and looking worried so they can't be too far away.
Here's the scene of them running through the forests:
The snow at Winterfell below the walls will be deeper as snow collects at walls so should help soften the impact.
So it appears they could survive the fall with the snow cushioning it but the amount of snow needed doesn't seem to tally up with what we see on screen.
All the way back in Season 1 Episode 1 we see Bran fall from a tower, of taller height, straight onto his back after being pushed by Jaime.
He is paralysed and put into a coma by this fall but does survive it. So it appears it is possible. Credit to @Flater for this point.
Another character that dies from his fall is Tommen Baratheon though he appears to fall from a much taller height.
From the books the perspective is a little differently. Though in the show the snow doesn't appear to be forty feet high at all.
"I saved her." The outer wall of Winterfell was eighty feet high, but beneath the spot where he had jumped the snows had piled up to a depth of more than forty. A cold white pillow.
Winds of Winter - Theon I
In World War II, multiple pilots survived falls of not just 100 feet, but over 18,000 feet without a parachute. If my memory serves correctly, the true story Under the Wire by William Ash (and Brendan Foley) tells at one point how William Ash met a Soviet prisoner-of-war who had fallen more than 20,000 feet from his bomber aircraft and survived by plunging into snow.
- Nicholas Alkemade apparently survived falling 18,000 feet into pine trees and soft snow.
- Alan Magee fell 22,000 feet and through the glass roof of a railway station, surviving but with many injuries.
There are plenty more examples.
If the snow's deep enough, they could easily survive a fall of 80 feet, regardless of plot armor.
This video shows a guy skiing away from a jump off a 255 foot cliff. He lands head first.