Fishing Little Red River

You are in prime trout country with literally world class browns. The brown trout have already spawned but should still be feeding. If you can throw something deeper that can move at the speed of the current (nymphs/streamers), I think depth matters more than pattern, you may be able to catch a nice one. Key is to get the bait deep and drift it in front of their nose. Depending on water temp the trout might be becoming less aggressive. Hope you can land a big one!

Fly fishing or spinning gear?

I tore up some rainbows on rooster tails a couple months ago. Didnt catch any at the state park but I walked south down the river at the Cow Shoals access until I got out of the catch and release area.

You can change it to catching , not fishing, get a trout magnet, in chartreuse and fish it on 2 # line 4 inches above the bottom.
This works every time as long as you can get it at this depth, use small slip lit shot if current is too strong.
Fly fishing is a waste of time.