Mud over rough pine?

Not a great plan.
Cover and finish them with sheetrock , with outside metal corners if you want them smooth.

I've mudded over wood without any problems. The rough cedar may be somewhat problematic as you will get pieces of the cedar in your joint compound and that will frustrate you to no end. At least sand it enough to remove some of the larger chunks that are bound to come off when you run your broad knife through the joint compound.

Another problem that may arise is that the cedar has oils/tannins in it that may wick into the joint compound. You may then have to prime with a stain-blocking primer to keep those tea colored stains from showing up in your primer and paint.

+1 sheetrock over the beams. You'll be glad that you did.

To drywall over the beams will give you a much better look and as stated no worries abut the bleed through. Just tape the inside corners and use bead on the outside corners.