Is it better to mill boards before or after drying? (And does it depend on diameter?)

Generally, it's far, far better to rough-mill while green, dry in a stack with stickers to allow airflow and if necessary considerable weight to put on the stack, then do final shaping with the moisture content near the desired environment.

First, it's much faster to dry the relatively thin rough boards.

Second, drying induces strains in the wood. By rough-milling and stacking the boards during drying, these strains will be (largely, most of the time) relieved. Milling a dry tree trunk is an invitation to wild distortions of the wood once it is free to move.

Frankly, I don't know if 4-inch diameter trunks would be all that badly affected. What I think is clear, though is that the wood won't look all that great. Early growth generally produces wide rings, and the very core (called the pith) is not normally used, and curvature of the rings is likely to cause ...unfortunate... wood movement in response to seasonal changes in relative humidity. Unless you quarter-saw each trunk to get two boards, one on each side of the pith (and so about 2 inches wide or less) you're going to get a lot of seasonal warping and cupping. This may not be an issue for things like picture frames, but you need to be aware of the possiblity.