Any horse should not be defined as skinny. Walker's a bred to be lean and long, yet I have two and they are chubbsters.
If I were you I would deworm your horse, then get some nice sweet grain just a normal sweet 12% then go from there. I suspect the horse has just been underfed and not dewormed. Good luck! And enjoy your walker, theyre amazing
I also think it depends on the pedigree of the TW. We had one that was very drafty even at 3 yrs old. But our other TW, Cherokee, is narrow framed. His top line is taking forever to fill out as well. He is now 7 yrs old and has a noticable difference in the width of his bones from when we bought him at 4 yrs old to now. He is starting to fill out more. He is well cared for, well fed and super healthy. Its just who he is and his genetic makeup that made him thin framed and a slow bloomer.