Is this a frozen pipe?

This is our third winter living in this house, an old victorian, and we have never had a problem with the pipes before. Last night we had a cold snap(-17C) and my bathtub hot water tap won't work. The toilet isn't flushing either. The water comes in, but nothing will leave the bowl. I turn on the hot water tap in the tub and nothing comes out...not even a drop. I thought only cold water pipes froze. The tub is on an exterior wall and the pipes run behind it. The water is fine in the rest of the house, all except the pipes running in my bathroom, which is situated on a north facing wall. The water in the bathroom sink...in between the toilet and tub...works fine. I'm confused, is this caused by a frozen pipe?