Never snapped a rod icefishing (knock on wood)...but then again I use appropriate gear for the appropriate targets.
But I would recommend getting 2 rods with different action.
1) UL or L for sunfish, crappie, perch, cisco and even whitefish
2) ML or M for whitefish, lake trout, pike and burbot.
The action has less to do with whether the rod can sustain the fish on the run...but rather detecting bites and sustaining allowing you to set the hook on the bite.
Too soft a rod and you have a weak hookset on larger fish with bony mouths, especially when using lure that have stout hooks intended for larger fish. If you try to set the hook to hard, then you risk snapping the rod on the hookset. You can always ease the drag when you fight a fish, but if you ease the drag on the hookset, you simply won't set the hook if the hook finds cartilage.
Too stiff a rod and you pull the hook out, or rip right through, fish mouths, especially smaller fish like perch, crappie and cisco. It will be more difficult to detect a lift bite that is so typical of perch, crappie, cisco and whitefish. You may just barely see the line slack for a second but the tip of the rod will not bend. With a soft rod, even smaller lures will keep the rod tip bent. When a fish picks up the lure, you will see the tip bounce up but the line is still relatively tight. You can set the hook (if you have fast reflex) immediately on these lift bites.
