NO NO NO!! Keep the snorkel out! It won't hurt anything. Very few will disagree, but the snorkel is there only to keep the noise levels down. Some people believe it is there to keep out water, cigarettes, etc...but the snorkel is cupped on the end and if you think about it with actually HOLD water.
I've been de-snorkeled for 2 years now, daily driver, 12,000 miles per year, in Chicago. So I have been through all types of weather. Nothing has ever given me problems. Not rain,snow,or sun

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So keep the snorkel out, replace the stock filter, and be done with it!