My basement drain is backing up a bit recently. Before I call a plumber, or rent an electric sewer snake from Home Depot, can sewer pipes freeze? It is January after all (and my house is in Canada).
Drain pipes are generally run below the "frost line" for the region, and should never freeze in anthing resembling a normal winter.
Yes they can, especially in exposed areas. I've heard of sewage pipes freezing in the winter and backing up into apartments in NYC, with disastrous consequences, though the more likely culprit is something that was poured down the drain.
You could always pour some boiling water down the drain to see if it would help.
Fat and grease is another common enemy for drains. It might be hot/semi liquid when it goes into the drain but once it hits the colder sections outside it quickly cools and solidifies. This is sticky stuff and attracts debris, building up over time. Google (images) 'fat berg' if you totally want to be grossed out!
It seems to be a fact of utility life that people have forgotten what drains are and how they should be treated. Young people especially treat the toilet like a dustbin in my experience.