Can Endermen build Snowmen or Iron Golems?

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.

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.

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.

This video shows them making iron golems, which then attack the endermen:

Note that this isn't even with the iron blocks systematically arranged in T's.

You know those carpet-like blocks that are snow? use them. They can't create golems from that type of snow. You will need silk-touch however.