I store mine inside for the winter and I cover it despite the fact it is inside. Keeps barn dust, bird do-do, etc. off it. I put it away clean and it is clean when I retrieve it.
For years I stored rigs outside in winter. I always covered them when stored outside as well.
Putting the cover on takes maybe 30 minutes of my time, taking it off maybe 20 minutes. Is it a hard job? I guess it could be if you wanted it to be.
I have never had paint damage from the cover but the cover has prevented countless hours of sun, hail, freezing rain and snow from damaging my rig.
Leave it exposed to harsh winter weather or protect it? Seems like a no-brainer to me!