Does this sign prohibit continuing if you do not have snow chains?

A)No, as this sign only recommends the use of chains.
B)Yes, in any case.
C)Yes, unless you have other equally effective authorised devices.Correct
The sign in the question indicates the obligation not to continue without snow chains or other authorised devices acting on at least one wheel on each side of the same drive axle.
You may continue when you have one of the following authorised devices fitted:
- Snow chains.
- Other authorised devices, such as textile covers.
- Winter tyres (MS), specially designed for snow and mud.
- Studded tyres, whose studs must have rounded edges and must not protrude more than two millimetres above the surface.