Of course without seeing it first hand, it's hard to say for sure, but just looks like overgrown, unshed frog to me. If you were to clean/scrape out his feet before taking the pics it would help too. He just looks way overdue for a trim but also has long & underslung heels. I doubt they would have become like that by only 10-12 weeks from the last *good* trim. **If it's what it appears to me*, I would just pare that flap - and any other loose bits - off the frog with a knife or nips.
While I'm not condoning the farrier's lack of apparent responsibility, remember it is christmas & he may not be working ATM. I would not like to judge him based just upon this information, but I would be looking to educate yourself, so you can better judge whether he's doing an adequate job or not. Hoofrehab.com is a great place to start.