They will build up strength in time, but sometimes that transition is several months in the making. Whether or not you put shoes on him should be determined between you and your farrier. There are some horses who can't seem to stay sound without shoes and there are many who never take a lame step barefoot. If you want to give him a shot barefoot, then by all means go for it. You can always add shoes later if barefoot doesn't work for him.
Lots of riders pull their shoes in the wintertime. The horses aren't getting used nearly as much or as hard, plus bare feet have much better traction than steel so the chance of slipping and getting an injury is lowered without shoes.