It depends on the plant. The frost tolerant ones might survive, unfortunately most will cop it! Sorry to be the bearer of bad tidings........

This will depend on a lot of variables, John, including the temperature that the soils falls to and the length of time that the soil is frozen. There are two forms of damage. One is damage to the cell structure of the plant but the other is lack of water. When the soil becomes frozen there is no free water for the plant to take up and it will droop.
I have two houses full of plants plus cold frames etc. These have all been frozen solid for over a week now and look like remaining so for a further week, at least. I will definitely have some losses but am (always) hopeful that the majority will be OK.

I agree with Bulbaholic. after all plants have to cope with frozen soil in nature anyway, some survive and some dont.

Most plants out in a garden have fine roots which penetrate quite a way into the soil. Therefore, even when the top few inches are frozen solid, if they are hardy, they still survive with the roots able to take up nutrients and water.
In a pot, the entire compost can be frozen solid and as Bulbaholic says, they can die from lack of water.
I never seem to get used to the fact that on very cold nights in winter the frost will penetrate a greenhouse AND a frame in which my plants have been located, and the compost is frozen solid.
Expensive though it works out, a little gentle heat from underneath achieves miracles. I find those little tubular heaters (about 150 watts) marvellous, if fastened below staging or in contact with a metal tray. But as with anything electrical, make sure you switch off the power completely in the greenhouse before doing any watering.