It depends on what you mean by biome, If you are meaning what is says in the F3 Menu, then no it will not change it, neither will putting snow in a large area will make it snow.
I made a plain biome by burning down a forest. The mob spawning actually increased when that happened. Other biomes no clue inly turn plain into forest and forest into plain.I meant only not inly.
Biomes are specific to the seed. One can change the look of a biome in a way, but usually biomes are categorized by the color of the grass and the stuff that spawns there. Could you make one biome look like another? Possibly, however putting snow on a plains biome will not make it a snow biome, it will just be a plains biome covered in snow. Everything you'd need to know and more right here. Just give a click.
I feel stupid for asking this, but I gotta find out somehow.
it depend if you feel it is new biome or not. But try making new biome such as rainforest. forest with snow. Just an idea