I know you've already gotten several answers but my my first impression when looking at the picture you posted was simply "pretty".
Nice to have access to places like that. You're a lucky person to have these locations close to you!
Joe Bertolini
I'd call it a "crick" and wouldn't tell anybody about it !!!!!!!!!!!!!!!!!!!
"Tap her light and she'll always be fresh"
Ironically, my dad used to own property in Upstate NY and had a stream pass through the property that had a bit more water than that. He told me he started seeing fish swimming in the stream a few years before he sold it. I didn't really believe him. He had the property about 15 years with nothing but tadpoles ever seen in the water. Didn't think it had enough water in it to support fish even though we had a pretty good "pool" on our property (was about the size of a large kiddie pool, good for cooling off when it was hot, much too small for swimming). I suspect someone probably stocked the stream during the early spring or late fall months when my dad would not be at the property (that lake effect snow is NO JOKE).
Edit: Forgot to add that about 10 years ago I would have named it: "Fishless"
Paul
I'd call it the Rose River.
I'd call it a "dribblutary".
Maybe this was already mentioned. I'd call it a 'Mountain Stream'
Where I grew up in New England, we'd have called it a babbling brook
aa
US Veteran and concerned citizen
Plain 'ole mountain creek to me.