Put a post on each side of the stream as close as possible and string your barbed wire...drill a hole in the bottom of each post and run a length of galvanized cable through it fairly close to the ground...build a fence panel out of pressure treated furring strips and hang them from the spanning cable with eye hooks...it presents a fairly heavy obstacle but will swing up and out of the way if the stream rises...I use this method on 2 streams on my property and have had no maintenance issues as it is self cleaning. I also left a couple of feet of slack on one side of the post with a clamped eye in it in case I ever need to take up some slack with a come-a-long. You can place a couple of short posts on the upstream side to keep the cattle from pushing it open (only swings one way).
I've seen a lot of farmers try many methods, and this one has worked the best. The wood I've seen has been 1x4 or 1x6 though. They stay clear of debris better than wire panels or gates.