Ive got two second cross beddy whippets, before them id had pure whippets. One of my whippets was a bit of a wimp with the cold but the other was tough as old boots. I recon one of the biggest advantages of havin the beddy in there is for abit more bone and also gives them much thicker skin, find this helps when there in think cover or when they have a barbed wire moment as the always do at some point!!
Id say having the bedlington defo gives them abit more bump proofing!