Yes you can have 2 Vivillon Patterns in your game at one time. In fact you can have all the different forms of Vivillon if you trade for them.
But No if you evolve a Spewpa in Frost Cavern it will not evolve into a Polar Vivillon. Vivillon's form is based on the location where the player is in the World such as in Mexico you can get Vivillon's Sun Form. If you want a Vivillon Polar Form you will have to trade with a player from either Norway, Sweden or from one of these locations in Canada or the USA.
Canada: Alberta, New Brunswick, Ontario or Quebec.
USA: Connecticut, Maine, Massachusetts, Michigan, New Hampshire, New Jersey, New York, Pennsylvania, Wisconsin or Wyoming.
Hope I helped :)