There design doesn't really yell "ice" to me. I looked up their origins and still no clear answer. Google search is out of the question since if you Google it the answer would be "because they can shoot ice out of their hands and mouths".
Sneasel may be based on the kamaitachi, a type of yōkai often represented as weasel demons with sickles on their front legs and sometimes understood as the cause of mysterious cuts on the skin, especially in cold weather.
Source
Weavile live in snow covered areas
A scratch from its claws will give you a case of frostbite!
Numerous Weavile entries reference it living in icy places as well.
Hope I helped!