From January to March, 40 Tribes (http://40tribesbackcountry.com) sets up a small luxury yurt-camp high up the Ak-Suu Valley that caters to advanced skiers and snowboarders. It's certainly not cheap, but it offers unique backcountry access and unparalleled comfort. Get in touch early, as their short winter season regularly books up completely.
Though a day trip from nearby Karakol is eminently practical, the beautiful location of Kara-Kyz Yurt-Camp makes an overnight visit appealing as well.
Facilities in the village are limited, so bring snacks or plan to order meals at your accommodation.