Can Endermen build Snowmen or Iron Golems?

There's currently two mobs that can be spawned by arranging blocks in a certain pattern: Snowmen and Iron Golems. If an Enderman produces this pattern, does it spawn a mob as if I had placed the blocks?

In other words: If I have a pumpkin farm next to an igloo, do I have to worry about my walls spontaneously turning into Snowmen?

Yup, they sure can!

And here's the reddit thread where they talk about it.

This YouTube video by KapitanWalnut proves that Endermen can in fact create Snow Golems, and by extension Iron Golems:

They can, as covered in the other answers.

However, Endermen cannot move snow or iron blocks; so they can only create a golem where the body pattern already exists. You could perhaps block such creation by ensuring there is always a block above any two-block-high section of snow, and so on.

Also, it is highly unlikely that an Enderman will pick up a pumpkin in the first place, and place it on your snow; you could make sure that there are no pumpkins near your base, and remove any you find moved closer by Endermen.

Yes, according to the Wiki:

Enderman are able to create snow golems and iron golems if they pick up a pumpkin and set it on already placed snow or iron blocks.

Haven't seen it happen myself, but seems plausible as they can move pumpkins.

They can make Snow Golems no problem, however the only way they can make Iron Golems is to place a pumpkin on the iron part - they cannot pick up non-natural (player-created) blocks, and iron blocks are always player created.