Kyrgyszstan travel alone

Absolutely - I've travelled around many times, and it's been absolutely safe. You might get the occasional bit of verbal hassle, and people will be very interested in why you're travelling (and where your family is!) but nothing more than that. The only thing I found about solo travel in Kyrgyzstan was that transport could be a bit of a pain. Marshrutka is fine (cheap and straightforward) but for places where there's no service you have to get a shared taxi, and if there's only one of you it can take forever to get other passengers! Similarly with treks, you usually can find other people to join up with but you need to be pretty flexible about timing and be prepared to hang around if necessary. The best trekking and horse trekking I did was south of lake Issy-Kul (organised by CBT Bokonbaevo) and around Kyzyl-Oi, but Karakol and Kochkor are also both good places from which to organise treks. The CBT office wherever you go will have lots of ideas - good luck!