Verb meaning "to partially hide"?

Obscuring -- Obscure: indistinct to the sight... dictionary.reference.com.

Or how about misting -- this would imply the feeling of steam condensing on your faces as well.

I would suggest using a figurative, 'veil' verb, unless you want a literal word.

Example from "Rise and Shine" by Anna Quindlen on Google Books

The coffee was strong, and the steam veiled our faces as we bent over it.

Veil on The Free Dictionary

v. veiled, veil·ing, veils v.tr.

1. To cover with or as if with a veil: Dense fog veiled the bridge.
2. To conceal or disguise: a smile that veiled his anger.

"while the steam blurred our faces..." or "while our faces were blurred in the steam."

blur - "to make dim, indistinct, or vague in outline or character" MW

• The tears in my eyes blurred the words on the page.
• His novel is based on historical occurrences but it blurs the line between fact and fiction.

I am inclined towards 'shrouding'. It even alliterates with the previous word, adding to the sentence's elegance.