Try tapping on the tuner module with something like a toothbrush to see if this gives any interference/dropout.
If so, usually it's bad solderings mostly on the edges of the pcb inside the module, where the pcb is soldered on the metal surrouding (you could check this with a magnifying glass).
Another troublemaker on that IF board is that big IC TDA8120 (or TBA ?); if it always goed the same way: cold start = problem, after a few mins = ok, try spraying that IC with freeze spray and see if the snowy picture returns when the IC get's cooled.