Not quite. "I'm afraid we're in for a storm." is usually a metaphor, or a comparison to something that it is not. In this case, a "storm" usually means something bad in a person's life. Sally looked up from her book, frowning, as Kate entered the room. "It's over!" Kate wailed. "They're coming!" Sally closed her book, taking a deep breath to steady herself, and stood. "Well. I'm afraid we're in for quite a storm now." In this case, the "storm" is the people invading their house, but it could be anything, depending on context, like a heavy week of schoolwork or anger from someone you know. It could also be an actual storm. Depends on context. :) The other two sentences are similar, but are not written in the common styling. "Facing a storm" is very similar, but sounds strange, and "Meeting a storm" implies that the storm can talk and you would like to shake hands with it.

"I'm afraid we're going to face a storm" and "I'm afraid we're going to meet a storm" do express the same idea, and with correct grammar, but the expressions are not colloquial. If you said either of those, you would be understood, but someone might look at you strangely.