Air Lock: Mummies "lived" in tombs for thousands of years. There is no such thing as weather in a tomb, so when the mummy goes outside, he brings with him a power that disables all kinds of weather.
Dry Skin: The body and bandages of a mummy are very dry. A fire attack would harm this Pokémon greatly, like it was Super Effective. Water on the other hand would hydrate it's body again and bring him back to life a bit.
Insomnia: Mummies have been "sleeping" for thousands of year. Now that they're awake, they're not just gonna get put to sleep again. They'll be awake forever.
Snare Trap/Entomb: The body of a mummy is wrapped up in bandages. He can use these bandages to trap and hurt other Pokémon like he was carrying chains.
No Ability: None of these abilities really fit this Pokémon, while Shed Skin, the ability he already has, is just perfect. So there's no need for another ability.
Just as a note. These aren't my opinions. These are just the general reasons why these abilities are chosen to fit the mummy best.