In the first seven months of 2012, the country of Georgia, sandwiched between the Caucasus Mountains and the Black Sea, saw a 54 percent increase in visitors, including savvy Europeans taking advantage of budget-friendly flights and a straightforward visa system (360 days, issued on arrival) to bask on Black Sea beaches and tour ancient castles. Now tourists are coming in winter to explore what Georgia is touting as the Switzerland of the Caucasus: the ski resorts and backcountry of the country’s 16,000-foot peaks.

While it’s just five years since the brief war with Russia over the separatist states of Abkhazia and South Ossetia, and the country borders the still restive republic of Chechnya, the situation in Georgia remains stable and safe. Lucky for you, because there is endless, pristine mountain terrain to explore. Fly into Tbilisi and head 75 miles north to Gudauri, where recent upgrades include a high-speed lift, a gondola, and hotels like Carpe Diem, a modern lodge steps from Gudauri’s lifts (doubles from $195). Enjoy a day of scenic groomers (lift ticket, $18) or try Heliksir for laps on untracked 13,000-foot peaks ($847 per person per day). The more intrepid should consider heading north up the partially paved Georgian Military Highway to the adventure hub of Stepantsminda, where experts can ski-mountaineer 16,558-foot Mount Kazbegi with Mountain House outfitters and anyone can snowshoe up to the 14th-century Gergeti Trinity Church, above town. Warm up again at the Rooms Hotel (doubles, $130), a slick new Aspen-style lodge.