Looking on the internet deeply has found these results:

Go horseback riding is the most popular phrase on the web.

Do horseback riding 123,000 results on the web	Go horseback riding 1384,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
He went horseback riding last night. I've gone horseback riding. I can't do that. Skydiving... piloting a small plane, and horseback riding in Mongolia... I can't do any of that. I don't think he'll be going horseback riding anytime soon. I'm more into fast action sports like horseback riding or skiing. Tuesday he took his grandkids horseback riding. It's a perfect night for horseback riding. We were just in horseback riding club together in college.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Do horseback riding

123,000 results on the web

Go horseback riding

1384,000 results on the web

More popular!

He went horseback riding last night.
I've gone horseback riding. I can't do that.
Skydiving... piloting a small plane, and horseback riding in Mongolia... I can't do any of that.
I don't think he'll be going horseback riding anytime soon.
I'm more into fast action sports like horseback riding or skiing.
Tuesday he took his grandkids horseback riding.
It's a perfect night for horseback riding.
We were just in horseback riding club together in college.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.