If you're looking for an experience with a difference, you definitely need to try a dive in Lake Baikal during winter. With an average depth of 744 m (2,442 ft), the lake freezes at times, just enough to be crossed on foot. Be careful though, temperatures can drop as low as -19°C (-2°F), and frostbite and hypothermia may occur.
Even in May, the waters of Baikal measure a temperature of around 2°C. Divers often use under-garments and electric heating wear, especially when diving under the ice. The best month for ice is March, when it's 80-120 cm (31 - 47 in) thick and safe to walk on. The hot spots are Listvyanka, port Baikal, Bolshie Koty and Railway.
Baikal is not really the place to be for a very deep dive though. The diving record stands at only 154 m (505 ft) in a 1°C (34°F) water, Gennady Misan being the protagonist. BaikalTek offer dives with depths from 3 m to 30 m (~10 ft to 98 ft) for around 45 minutes, depending on weather conditions. Make sure you bring suitable clothes and enough hot drinks to keep you warm; Russian winter is one of the toughest, and it doesn't forgive the unprepared.