The dead men cannot pass the wall, that is true. Wall was enchanted with ancient magic by its builder to stop the dead men from coming.
But the Wall is not eternal. It can fall. The others will not try to pass through the gates, they will try to bring it down. We know it can be brought down by magical weapons such as Horn of Joramun which according to legends has the power to bring down the wall.
According to GRRM:
“The Others can do things with ice that we can't imagine and make
substances of it."
Winter has finally come which means more snow and increase in power of the others.
- They might make an Icy bridge or stairs over the wall to cross it.
- They might freeze the sea to build an ice road which takes them over the water and lands them on East Watch by The sea.
- They might build a bridge across the sea all the way down to South.
- They might bring down the wall using Magic and horn of Joramun.
- Others have Ice Spiders according to the legend. With it being Being a spider, it is safe to assume the beast might be able to climb over the wall with its rider.
- The wall is not complete. There is a dangerous way to by-pass the wall which has been used by Wildlings to raid and attack the Seven Kingdoms. The region is called the Gorge. It can be used to sneak inside the realm without having to trouble with the wall at all. But only surefoot and strong people can cross it, it's not everyone's cup of tea.
- Others might try to infiltrate the wall. They have successfully demonstrated that before during the assassination attempt on Jeor Mormont which happened when NW men brought corpses of dead brothers inside Castle Black and at night they rose to kill the Lord Commander. So it appears, others can enter the Wall if a man of the Night's Watch escorts them.
If Wall is not defended by Might of all Men, Others will find a way to by pass it and continue their war against Life.
According to Books however, there is one more point:
"He's some dead thing. The monsters cannot pass so long as the Wall
stands and the men of the Night's Watch stay true, that's what Old
Nan used to say. He came to meet us at the Wall, but he could not
pass. He sent Sam instead, with that wilding girl"
There are two prerequisties for the Wall to deny entry to the others.
- Wall has to be standing.
- Men of the Night's Watch have to be true.
As of now, Men of the Night's Watch are not true. They have mutinied twice and killed two of their Lord Commanders. It is very important that Men of NW remain true because if any of them escorts the Others inside, Enchantments won't stop them.