The only difference in cleaning with weather is the viscosity of your lubricant. Other than that, you shouldn't have any difference.
As far as a rust preventative, there are myriads of choices. A lot of people say Eezox is the best, or other pure rust preventative for putting on exterior, non-action parts, like the barrel on your shotgun. If you can get BreakFree CLP, that is a good all around product but it is not the best at any of the three things it is supposed to do (clean, lube, preserve). It is a jack of all trades, master of none type of product.
I personally, on my Mossberg 500, just use BreakFree LP (not CLP), for lubricant and preservative duties. Cleaning, I usually just use Hoppe's #9 solvent if it gets real dirty or I have shot upwards of 500 rounds through it. If not, I just wipe it down real good with a rag and then give it a light layer of the LP.
Damian