Covers effect the tone slightly, they roll in the highs and warm up the bass, kind of instant vintage vibe :) so players who remove a cover often comment on how much more 'air' or presence they can hear.
As Bigsteve pointed out I can compensate in the wind for this, some models like the Mule I actually voic with a cover.........open Muls are a touch hotter to create the same tone.
Covers offer protection from sweat and grim also RF too. Raw nickel silver is sonically the most transparent, nickel and gold plate next with chrome having the most attenuating effect as it's the heaviest plate.Some players claim chrome is brighter.................shinnier yes, but not brighter in my experience.