If the horse is still that thin, stop riding him till he gains more much needed weight.
Take him for walks to build a topline...it is absolutely possible.
But a skinny/thin horse needs to use every calorie they eat to gain and heal their bodies first before you start working off what you are striving to fix and replace.
It takes months to replace, replenish weight on a "thin" horse for whatever the reason.
A ill fitting saddle is just one more reason to stay off the animal...
But yes, any saddle you use now while the horse is recuperating is often not going to fit as the horses condition improves...
Having to cinch down a saddle that tight is doing more damage than good, period.
As the body heals amazingly the topline fills in and develops...it takes good nutrition to build muscle and a layer of fat on the body... that takes months to accomplish, many months.