I don't know if I have any information that will help you or not. You asked for Rawson's in Fremont County, Idaho. Most of the Rawson's from my side of the family were raised in and around Egin and Plano areas. This actually puts them in Madison County. My Grandfather's and Grandmother's names were Joseph Harry Rawson and Pauline Alberta Mayne Rawson. Harry Rawson (who was Joseph's father) also died in Plano Idaho. If this is kind of what you're looking for, please send me an e-mail and I'll see what I can do for you.
Sincerely, Brenda Dixon