If you can find a larger project where you can leave at least one weathered edge intact (as mdntrdr mentioned) that would best show off the age of the wood. How about some benches using a cut edge for the seat.
If there are too many cracks/splits to resaw into larger pieces, cut it into small pieces you can use for many different projects from frames, small boxes, planter boxes.
Do you know the wood species on your beams?
I've been using a lot of white oak from our old barn for projects. I plane off the greyed weather outer edge, but still get a lot of color variation/staining from tannins a inch or more into the wood. Best of both worlds - I still get a weathered look, but have smooth straight edges to build things with. There is obviously a lot of waste in getting usable boards, but it was free to start with so it really doesn't matter.
"Good Behavior is the last refuge of mediocrity" -- Henry S. Haskins