Alright, after some testing I know the answer. No, Refrigerate will only come in effect if Nature Power turns into a Normal type move (like Tri Attack).
Source: I tested it against some Trevenant in the winding woods. Because this was in grass it turned into Energy Ball, and was not very effective against them (Grass resists Grass). So it obviously did not turn it into an Ice type move (which would have been super effective).
Hope I helped.