There is generally no issue (i.e. no significant ice is picked up) with a brief penetration
of a thin layer of stratus, e.g. 2000ft thick.
IME, anything which has holes in it so you can see the blue sky above, and given an absence of frontal weather, is not a problem.
But
enroute you will pick up ice eventually; no argument there. I always have, though sometimes it took half an hour to see it. Sometimes it is rapid; I have seen 1" in 5 minutes, in a layer of NS.
This is the problem with using the IMCR in the winter. You cannot go into Class A, cannot go into most Class D for long periods, so you end up stuck in icing conditions. Whereas if you had an IR then you just file for FL100 or whatever and climb up straight through it.
The other problem with this kind of wx is that with surface temps around or below 0C you have no escape route if you pick up too much and let it get out of hand. You will have to land with whatever you have picked up - unless you manage to get VMC on top in which case you can let it sublimate away (but that takes ages).