V70, freezing A/C system (manual A/C)?

Hi, A/C in my car behaves like this: A/C will start cooling and for about 10 minutes appears to be okay. But after that the air stops coming out of vents. If you take a look under the hood, all pipes/hoses are covered by thick layer of ice (even on hot summer days). I imagine the evaporator is also covered by ice and the air simply can't get through it. If you stop the engine for let's, say 15 minutes, ice melts down and all of that starts again.
Important note, when I try to turn the A/C off by pressing the button, the compressor is still working - like the clutch doesn't disengage immediately, you must turn the engine off (I don't know if this is normal).
Please, can you give me some advice? I have no idea.