Fire your snowshooter and Frostwind will fall down and flee. When you reach the second room that has the caged hostage, shoot the Frostwind's head when it appears.
The 5th level in the town's Snow Gate is the Frostwind Boss Battle. This seems hard at first, but there is a strategy to defeating him easily. When you start, Frostwind pops out of a hole. Blast him with your Snowball Cannon and he will go back in. The screen will then move to the right. Jump over the hole so you don't fall, and continue right. Keep to the right as Frostwind will appear on the left-- make sure you can see where you're going. After evading his bites, he will fly across the top of the screen and do a headfirst dive into a hole. Repeat this process untill you switch to an alternate area. Frostwind will now have a health bar. Above is a captured Rappo in a dark cage above. Frostwind will fly into one of the holes, then come out and fly overhead to the other hole, shooting ice spikes along the way. Stay in front of the center rock and you will be safe. After he flies into the opposite hole, he will pop out once again. Don't shoot him as that will not damage him. After coming out he will shoot a single ice spike. Evade it, and he will go back in. Stay a short distance past the middle rock, and Frostwind will come out and try to bite you. After you have dodged that, shoot him immediately. If you timed it right, Frostwind will fall forward. Quicly Ground-Smash his head and it will take about 1/4 of his health away. After doing so, he will fly overhead like the previous time. Repeat this process, and he will die. The Rappo will be freed and this means you have won. Notice that when Frostwind is pursuing you from the left in Area 1, do not shoot snowballs at him as Frostwind does not have a health bar yet. So no atacks will hurt him. Also, in Area 1, Ground-Smash on any Snow Pile you see and keep them in a good number (25+ will do fine).