Need more info...how many, size, orientation and U-factor for the windows, R-factor of ceiling insulation, and walls, and floor if it isn't enclosed. You need a heat load calculation - you can find calculators on the web that are fairly accurate. Then, you can figure out how many BTU/hour you need for both cooling and heating. Anything done before that calc is a WAG, and basically a waste.
Before you start cutting beams, you may want to consult with a structural engineer. Also, your existing a/c and heating plant may not have enough reserve to support the room addition. You may wish to consider one just for that room, or take this opportunity to upgrade the system you have to a more efficient system that can handle the new conditioned space.