Ice types are very rare at the start of the game until you reach further. I know how disappointing it could be. But, that doesn't mean it's impossible to get at the starting.
Actually, the easiest Ice type you can get in Pokemon Rumble World (without spending anything) is Cubchoo from the "passcode gift". Go to wherever they ask for a password, and enter this code: 61211248.
It gives you a Cubchoo with 225 Attack, Effective - Special Trait, and the moves: Icy Wind and Ice Punch
But, if you want to find the balloon with the cheapest Ice type - from my experience - it would be "Pearl Marsh" under the Pearl Balloon (Palkia's). Here you need to land on the "Aurora Ice Field" to find the ice types. This balloon costs 50 PokeDiamonds and you can find 10 different ice type Pokemon:
Hope I helped! :)