Below is some snakehead info from US Fish & Wildlife. It appears that at least one species can live under ice (end of second paragraph). The full document is here. It's a real snoozer. http://policy.fws.gov/library/02fr62193.html
Two larger snakehead species, Channa marulius and C. maruloides, superficially resemble the native bowfin, Amia calva, in that all three are elongated fishes, have long dorsal fins, tubular nostrils, and an ocellus (eyespot) at the base of the upper portion of the caudal fin. The bowfin, however, has its pelvic fins in a more abdominal rather than thoracic or anterior-abdominal position, and the anal fin is not elongated. Moreover, the bowfin does not have a rosette (circular arrangement) of enlarged scales on top of the head.
Species and species complexes of the genus Channa are native from southeastern Iran and eastern Afghanistan eastward through Pakistan, India, southern Nepal, Bangladesh, Myanmar (Burma), Thailand, Laos, Malaysia, Sumatra, Indonesia, and China northward into Siberia. Of the currently recognized 25 species of Channa, 9 species and representatives of 4 species complexes occur in peninsular Malaysia, Sumatra, and/or Indonesia. Of the same 25 species, 16 species and members of 5 species complexes are tropical to subtropical; members of three species complexes are temperate; and one species is temperate to
boreal and can live beneath ice in the northern portion of its range.
The three species of Parachanna are native to Africa and are tropical. Snakeheads are considered as non-ostariophysan primary freshwater fishes (Mirza, 1975, 1995), meaning they have little or no tolerance for seawater. Habitat preferences vary by species or species complex, with a majority occurring in streams and rivers. Others occur in swamps, rice paddies, ponds, and ditches. All can tolerate hypoxic (low oxygen) conditions because they are airbreathers from late juvenile stages. Where known, pH range varies by species with one (Channa
bankanensis) preferring highly acidic (pH 2.8-3.8) waters. At least
three species are tolerant of a wide pH range; C. gachua, C. punctata, and C. striata survived for 72 hours at pH levels ranging from 4.25 to
9.4 (Varma, 1979).