Stainless sure doesn't hurt, but it's not essential. The key is good maintenance. To keep the wood in good shape, make sure that it's 100% sealed from outside moisture with either a polyurethane clearcoat varnish or a thorough rubbed oil finish (like tung oil). Either will seal the wood and keep moisture out.

For the blued steel, a high quality gun oil with good preservative properties is essential, and should be applied as often as warranted by conditions. Personally, I very much like BreakFree CLP (CLP mean Cleaner-Lubricant-Preservative). BreakFree CLP is commercially branded version of the milspec CLP that is issued to all troops for use with the M16 variants. It's basically a Teflon impregnated light oil/solvent mixture. It'll dissolve a lot of crud to clean the weapon, the oil provides immediate lubrication, and if applied correctly (meaning sparingly), it'll dry to a non-dust attracting coating that provides adequate lubrication (remembering that the M16's are select-fire weapons capable of full-auto/burst fire), and very good protection against the elements. If you're hunting in bad weather, you'd just need to dry the moisture from the rifle and reapply a light coat of CLP every day. It's also not a bad idea, if the rain is really pouring down, to shelter the rifle from as much rain as possible so as not to totally water-log it.

But if you like stainless steel, go for it. Just a side note, though. The type of stainless steel they make guns out of (usually 410 or 416 stainless) is not the same stainless steel your forks and spoons are made of. Firearms stainless CAN RUST. It takes a lot longer, and requires much more extreme conditions and/or neglect, but it can happen. So buying a stainless barreled action is not a ticket to getting out of gun maintenance. I am personally a very big fan of the stainless/laminate look for rifles. It's both an aesthetic and practical thing.

Mike