Rick Beato has a strumming exercise that would probably help:
https://www.youtube.com/watch?v=2FTndcu891g
That's what I think of as Step 3 of learning to cowboy strum. My steps are:
1. Learn the chords of an easy three-chord song.
2. Learn to play them in time, without breaking the rhythm — even if it means just playing the chord once before grabbing the next chord.
3. Learn a steady strum. It can be Rick's or one you make up yourself. What matters is that it's steady. Notice that sideways windshield-wiper motion he's using. It's easy, it sounds good, and you don't get tired.
4. Vary your patterns, and give different beats different emphasis. The idea is to start adding some expression and feeling to the chords.
5. Add songs that teach your more chords, like minors and sevenths.
6. Experiment with picking fingers up and putting fingers down in different places. For instance, play a D chord. Then lift your finger off the first string and play it again. Then put your pinky down on the first string, third fret. Then go back to the original D. You quickly learn what sounds good and what doesn't.
7. Experiment with hitting just one or two or three strings on some strokes — another way to vary it.
8.Find in-between bass notes. For instance, walk up from the low G of a G chord to the low C of a C chord. Or the low E of an E-minor to the low G of a G chord. Pay attention to which notes sound good and which to avoid as you walk up and down.
Put those steps together as you go. You'll find you can strum with feeling just about any folk, blues, or Americana tune.