Closest you can get to Kyrgyzstan experience in Almaty?

This summer (June), I'm planning to visit Central Asia, but due to a visa issue, I'll only be able to visit Kazakhstan and won't be able to visit Kyrgyzstan.
Scenery I would like to see is lush, green, alpine meadows, scattered tall trees, rolling hills, under snow-capped peaks, and a turquoise lake, so basically somewhat like Switzerland. I think I can find this scenery in Almaty in places like Kaindy lake, kolsai Lake, and big almaty lake.
However, I'm not sure if I can do activities in those meadowy places other than hiking. The activities I would like to do are horseback riding, archery, stargazing, and yurt glamping. All of them are experiences I can primarily have in Kyrgyzstan. Is there any way I can do this type of stuff near Almaty, Kazakhstan? I know Almaty isn't a tourist-heavy place and isn't really part of nomad culture, but I would still like to try something similar.