Engine snow dust protection (345 in this case) ???

I read a thread about the 500s needing a grill cover so I am assuming each model is different.

the grill on the 345 doesn't seem like it will need protection from snow dust as the kawi cooler air exits there and quite forcefully I might add.

But it looks like MUCH snow dust will enter through the hood slots pulled to the radiator screens by the cooling fan-

Is there enough heat from a warm cooler to melt the snow dust as it enters for say an hour or two in 0F weather?

Or is a foam filter required to cover the slots in the hood?

seems like ones that attach to the inside of the hood would work well.

any one with experience in this area?