They had iron anvils, yes.

In the time and place I study (early medieval England), anvils were pretty small, basically a large iron spike that would have been driven into a log or tree stump. Here's a photo of a 7th century example, along with an illustration from a few centuries later of one being used.

A small anvil like this could be made by any smith with a similar setup -- it's small enough that heating and shaping the metal would not be especially difficult.