The facts definitely matter and it will need to be disclosed when you renew your green card but generally - very generally - an arrest without a conviction doesn't impact a renewal (although it could impact an application for citizenship).
Because the ultimate legal issue is not whether one was convicted but whether one committed acts that would be considered criminal and so one could be arrested and not convicted or not even arrested at all but the record shows - or they inadvertently admitted - that they committed the elements of a crime. While it's rare that USCIS goes behind an arrest that didn't lead to a conviction, it can and sometimes does.
