I bought this 2006 F350 SRW used and it has 275/65-20 now. Looking at the option list it came with 18" wheels. I found a low mile set of 18" wheels with 275/70-18 studded snow tires. Will I see much difference between them? They calculate out about 1" shorter than the 20"set.

 

One it will help protect the rim, having more sidewall. And should improve ride quality some. Now maybe not studed tires, but if you but normal tires after on, again, due to taller sidewalls

 

I have a 2013 that came with 20" wheels and I run 18" in the winter with a set of studded winter tires. No noticeable difference except the speedo and ODO are off a bit. Ride is about the same as far as I can tell.